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In mathematics, a hypergraph is a generalization of a graph in which an edge can join any number of vertices. In contrast, in an ordinary graph, an edge...

In graph theory, a matching in a hypergraph is a set of hyperedges, in which every two hyperedges are disjoint. It is an extension of the notion of matching...

theory, a balanced hypergraph is a hypergraph that has several properties analogous to that of a bipartite graph. Balanced hypergraphs were introduced by...

mathematics, the hypergraph regularity method is a powerful tool in extremal graph theory that refers to the combined application of the hypergraph regularity...

theory, Hall-type theorems for hypergraphs are several generalizations of Hall's marriage theorem from graphs to hypergraphs. Such theorems were proved by...

In graph theory, a vertex cover in a hypergraph is a set of vertices, such that every hyperedge of the hypergraph contains at least one vertex of that...

In mathematics, a packing in a hypergraph is a partition of the set of the hypergraph's edges into a number of disjoint subsets such that no pair of edges...

relating the maximum matching size and the minimum transversal size in hypergraphs. This conjecture first appeared in 1971 in the Ph.D. thesis of J. R....

In graph theory, a d-interval hypergraph is a kind of a hypergraph constructed using intervals of real lines. The parameter d is a positive integer. The...

theory, there are two related properties of a hypergraph that are called its "width". Given a hypergraph H = (V, E), we say that a set K of edges pins...

Altair Engineering Inc. is an American multinational information technology company headquartered in Troy, Michigan, that provides software and cloud solutions...

In graph theory, the term bipartite hypergraph describes several related classes of hypergraphs, all of which are natural generalizations of a bipartite...

to reduce and explain all the laws of physics within a paradigm of a hypergraph that is transformed by minimal rewriting rules that obey the Church–Rosser...

Discrepancy of hypergraphs is an area of discrepancy theory that studies the discrepancy of general set systems. In the classical setting, we aim at partitioning...

In graph theory, the hypergraph removal lemma states that when a hypergraph contains few copies of a given sub-hypergraph, then all of the copies can be...

In the mathematical theory of hypergraphs, a hedgehog is a 3-uniform hypergraph defined from an integer parameter t {\displaystyle t} . It has t + ( t...

independence complexes, flag complexes, Whitney complexes and conformal hypergraphs are closely related mathematical objects in graph theory and geometric...

The Symmetric hypergraph theorem is a theorem in combinatorics that puts an upper bound on the chromatic number of a graph (or hypergraph in general)....

model a hypergraph in which U is the set of vertices of the hypergraph, V is the set of hyperedges, and E contains an edge from a hypergraph vertex v...

for hypergraphs are in general much harder than for graphs. Unlike graphs, hypergraphs admit multiple non-equivalent notions of cycles (see Hypergraph cycles)...

is an algorithm that applies to hypergraphs. The algorithm takes as input a hypergraph and determines if the hypergraph is α-acyclic. If so, it computes...

artificial intelligence and operations research, constraint graphs and hypergraphs are used to represent relations among constraints in a constraint satisfaction...

In graph theory, particularly in the theory of hypergraphs, the line graph of a hypergraph H, denoted L(H), is the graph whose vertex set is the set of...

induced Ramsey numbers to d-uniform hypergraphs by simply changing the word graph in the statement to hypergraph. Furthermore, we can define the multicolor...

theory. He is renowned for his research on Turán's extremal problem for hypergraphs. He studied mathematics at McGill University, where he earned a Bachelor...

contrast, a hypergraph can have multiple vertices assigned to one edge; thus, a general matrix of non-negative integers describes a hypergraph. The incidence...

application domains, with the input family of sets often being described as a hypergraph. In set theory, the axiom of choice is equivalent to the statement that...

hypergraph with n hyperedges, one may n-color the vertices such that each hyperedge has one vertex of each color. A simple hypergraph is a hypergraph...

open problem—of the "moderately interesting" rank—to be solved was in hypergraph theory: "A Constant-Factor Lower Bound For H (n)" by GPT-5.4. Longest...

mentioned in the above section on the algebraic approach to graph rewriting. Hypergraph grammars, including as more restrictive subclasses port graph grammars...

directed hypergraph where each hyperedge is directed either to one particular vertex or away from one particular vertex. In a directed hypergraph, each hyperedge...

Property B is equivalent to 2-coloring the hypergraph described by the collection C {\displaystyle C} . A hypergraph with property B is also called 2-colorable...

includes counting configurations of geometric shapes. Graph theory and hypergraphs Coding theory, including error correcting codes and a part of cryptography...

software modules, individual files, and events, associations, representing hypergraph relationships between topics, and occurrences, representing information...

The method of (hypergraph) containers is a powerful tool that can help characterize the typical structure and/or answer extremal questions about families...

plane (TPP), also known as a dual affine plane, is a special kind of a hypergraph or geometric configuration that is constructed in the following way. Take...

hierarchies. This approach leverages structures like simplicial complexes and hypergraphs to capture global dependencies and qualitative spatial properties, offering...

A classical approach to solve the Hypergraph bipartitioning problem is an iterative heuristic by Charles Fiduccia and Robert Mattheyses. This heuristic...

A hypergraph representing a family of union-closed sets. Vertices 1 and 2 (highlighted red and blue respectively) are present in over half the edges....

of edges. An r-uniform hypergraph is a set of hyperedges each of which contains exactly r vertices (so a 2-uniform hypergraph is a just a graph without...

envelope of lines determined by a support function Hedgehog (hypergraph), a hypergraph formed from a complete graph by adding another vertex to each...

3 {\displaystyle 3} -uniform hypergraph can have without containing the complete 3 {\displaystyle 3} -uniform hypergraph on 4 {\displaystyle 4} vertices...

A multi-hypergraph over a certain set V {\displaystyle V} is a multiset of subsets of V {\displaystyle V} (it is called "multi-hypergraph" since each...

for a k-uniform hypergraph. This formula is symmetric between vertices and edges which demonstrates a hypergraph and its dual hypergraph have the same cyclomatic...

This is a list of some of the more commonly known problems that are NP-complete when expressed as decision problems. As there are thousands of such problems...

chordal if the hypergraph of its maximal cliques is a hypertree. The name comes from the fact that a graph is chordal if and only if the hypergraph of its maximal...

two nodes, these are different edges. A multigraph is different from a hypergraph, which is a graph in which an edge can connect any number of nodes, not...

bipartite matching (also known as 2-dimensional matching) to 3-partite hypergraphs, which consist of hyperedges each of which contains 3 vertices (instead...

complete hypergraphs. The statement of the result is that if 2 ≤ r < k {\displaystyle 2\leq r<k} are integers and r divides k, then the complete hypergraph K...

into a space with Helly dimension 1. A hypergraph is equivalent to a set-family. In hypergraphs terms, a hypergraph H = (V, E) has the Helly property if...

generalization of graph bipartiteness testing to 3-uniform hypergraphs: it asks whether the vertices of a hypergraph can be colored with two colors so that no hyperedge...

line graphs of line graphs, line graphs of multigraphs, line graphs of hypergraphs, and line graphs of weighted graphs. Given a graph G, its line graph...

26 and preceding 28. Including the null-motif, there are 27 distinct hypergraph motifs. There are exactly twenty-seven straight lines on a smooth cubic...

problems can also be formulated as constructing the transversal hypergraph of a given hypergraph, of listing all minimal hitting sets of a family of sets, or...

bicriteria-approximation or resource augmentation approaches. A common extension is to hypergraphs, where an edge can connect more than two vertices. A hyperedge is not...

coloring is a generalization of the notion of graph coloring to hypergraphs. A hypergraph H has a vertex-set V and an edge-set E. Each edge is a subset...

In turn, the incidence matrix can be seen also as describing a hypergraph. The hypergraph includes one node for each element in X and one edge for each...

family of subsets of a finite set S {\displaystyle S} is also called a hypergraph. The subject of extremal set theory concerns the largest and smallest...

Lubell–Yamamoto–Meshalkin inequality. They may also be described in the language of hypergraphs rather than set families, where they are called clutters. The number...

PhD in 2004 under the supervision of Vojtěch Rödl. His dissertation, on hypergraph generalizations of the Szemerédi regularity lemma, won the 2006 Richard...

research accomplishments include results on the Szemerédi regularity lemma, hypergraph generalizations of Hall's marriage theorem (see Haxell's matching theorem)...

different notions of regularity and apply to other mathematical objects like hypergraphs. To state Szemerédi's regularity lemma formally, we must formalize what...

Arithmetic combinatorics Szemerédi regularity lemma Van der Waerden's theorem Hypergraph removal lemma § Proof of Szemerédi's theorem Erdős, Paul; Turán, Paul...

can be formulated as part of the theory of hypergraphs. A family of sets may also be called a hypergraph, and when all the sets (which are called "hyperedges"...

structure. The notion of laminarity can be applied to hypergraphs to define "laminar hypergraphs" as those whose set of hyperedges forms a laminar set...

structure constellations including directed, undirected, mixed graphs, hypergraphs, and application-specific attributes. A GraphML file consists of an XML...

definition of cutset for hypergraphs: a cycle hypercutset of a hypergraph is a set of edges (rather than vertices) that makes the hypergraph acyclic when all...

hypergraph, the tentacles carry labels which are determined by the hyperedge's label. A conventional directed graph can be thought of as a hypergraph...

linear graph form the hyperedges of a triangle-free 3-uniform linear hypergraph, and they form the blocks of certain partial Steiner triple systems; and...

graph characterization is a method of specifying a family of graph, or hypergraph, structures, by specifying substructures that are forbidden to exist within...

conformal field theory Conformal fuel tanks on military aircraft Conformal hypergraph, in mathematics Conformal geometry, in mathematics Conformal group, in...

the first open case (that of 3-uniform hypergraphs) of a famous conjecture by Ryser: in a 3-partite hypergraph the ratio between the covering number and...

the intersection graph of disks, and determining the probability that a hypergraph becomes disconnected when some of its edges fail with given independent...

refer to: related to hypergraphia, a behavioral condition related to a hypergraph in mathematics Hypergraphy, or hypergraphics, an experimental form of...

geometry. One can define a blocking set of a hypergraph as a set that meets all edges of the hypergraph. In a finite projective plane π of order n, a...

in high-degree hypergraphs is a research avenue trying to find sufficient conditions for existence of a perfect matching in a hypergraph, based only on...

{\mathcal {F}})} . Suppose the winning-sets are all of size k (i.e., the game-hypergraph is k-uniform). In a Maker-Breaker game, the Erdos-Selfridge theorem implies...

problem. Vertex cover problems have been generalized to hypergraphs, see Vertex cover in hypergraphs. Formally, a vertex cover V ′ {\displaystyle V'} of an...

structure than a linear space. The notion is equivalent to that of a linear hypergraph. Let S = ( P , L , I ) {\displaystyle S=({\mathcal {P}},{\mathcal {L}}...

problem, also called hitting set, can be described as a vertex cover in a hypergraph. Decomposition, defined as partitioning the edge set of a graph (with...

{\displaystyle o(n^{2})} error. Consider an h {\displaystyle h} -uniform hypergraph H {\displaystyle H} with v ( H ) {\displaystyle v(H)} vertices. The supersaturation...

new mathematical theorem with a proof in a work entitled "Forests with Hypergraphs". In 2011 she began studying mathematics at the University of Bonn. In...

of Economics. Her research involves graph theory, including graph and hypergraph packing problems, random graphs and random subgraphs, and the relations...

Processing Systems. 15. Zass, R; Shashua, A (2008). "Probabilistic graph and hypergraph matching". 2008 IEEE Conference on Computer Vision and Pattern Recognition...

products of graphs Walescki's theorem for hypergraphs: Do complete k {\displaystyle k} -uniform hypergraphs admit Hamiltonian decompositions into tight...

Lovász and Paul Erdős in the article Problems and results on 3-chromatic hypergraphs and some related questions. For other versions, see Alon & Spencer (2000)...

Tzevelekos "Full abstraction for nominal general references" 2008 David Duris "Hypergraph Acyclicity and Extension Preservation Theorems" 2009 Oliver Friedmann...

In the mathematical field of graph theory, a hypergraph H is called a hypertree if it admits a host graph T such that T is a tree. In other words, H is...

, k , r ) {\displaystyle T(n,k,r)} for r {\displaystyle r} -uniform hypergraphs of order n {\displaystyle n} is the smallest number of r {\displaystyle...

generalisation of the Oberwolfach problem for k {\displaystyle k} -uniform hypergraphs (for large n {\displaystyle n} ). Unsolved problem in mathematics Suppose...

described as one of finding the largest Berge-acyclic sub-hypergraph of a 3-uniform hypergraph. A hypergraph is a structure analogous to a graph but allowing more...

multiplication General-purpose computing on graphics processing units#Kernels "Hypergraph Partitioning Based Models and Methods for Exploiting Cache Locality in...

understand contextuality, from the perspective of sheaf theory, graph theory, hypergraphs, algebraic topology, and probabilistic couplings. Nonlocality, in the...

theorem on 3-term arithmetic progressions, and a generalization of it, the hypergraph removal lemma, can be used to prove Szemerédi's theorem. It also has applications...

Incidence structures use geometric terminology, but in graph theory they are hypergraphs and in combinatorial design theory they are block designs. They are also...

Series–parallel graph Threshold hypergraphs Reiterman, Jan; Rödl, Vojtěch; Šiňajová, Edita; Tůma, Miroslav (1985-04-01). "Threshold hypergraphs". Discrete Mathematics...

research concerns graph coloring, graph minors, extremal graph theory, and hypergraphs. He is known for the Kostochka–Thomason bound on clique minors and for...

Baranyai is best known for his theorem on the decompositions of complete hypergraphs, which solved a long-standing open problem. In addition to his mathematical...

mathematics. Aharoni, Ron; Haxell, Penny (2000). "Hall's theorem for hypergraphs". Journal of Graph Theory. 35 (2): 83–88. doi:10...

terminologies to describe these objects. In graph theory they are called hypergraphs, and in combinatorial design theory they are called block designs. Besides...

3-dimensional matching problem (3DM). The input to 3DM is a tripartite hypergraph (X + Y + Z, F), where X, Y, Z are vertex-sets of size m, and F is a set...

field of graph enumeration. More generally, the degree sequence of a hypergraph is the non-increasing sequence of its vertex degrees. A sequence is k...

at the Wayback Machine, Computerworld, 13 September 2007 "Patterns, Hypergraphs and Embodied General Intelligence", Ben Goertzel, WCCI Panel Discussion:...

playing on complete graphs, the clique game can also be played on complete hypergraphs of higher orders. For example, in the clique game on triplets, the game-board...

generalization of the mixing lemma to hypergraphs. Let H {\displaystyle H} be a k {\displaystyle k} -uniform hypergraph, i.e. a hypergraph in which every "edge" is...

Green–Tao theorem. In 2003, Gowers established a regularity lemma for hypergraphs, analogous to the Szemerédi regularity lemma for graphs. In 2005, he...

(1997), "Generating all maximal independent sets of bounded-degree hypergraphs", Proc. Tenth Conf. Computational Learning Theory, pp. 211–217, doi:10...

in as a part of a generic graph query engine, for performing graph and hypergraph pattern matching (isomorphic subgraph discovery). This generalizes the...

Quanwei; Li, KeYang; Pan, Lingfeng; Li, Xinyue; Hui, Mingxuan (2025). "Hypergraph Neural Network-based Multi-Granular Root Cause Localization for Microservice...

a sequence Discrepancy theory in structural modelling Discrepancy of hypergraphs, an area of discrepancy theory Discrepancy (algebraic geometry) Discrepancy...

networks Fractional stable paths problems Fractional hypergraph matching (see also the NP-complete Hypergraph matching) Fractional strong kernel Scarf's lemma...

site percolation, hypergraphs, and directed graphs. The original disproof is based on a small counterexample in the 3-uniform hypergraph case with 10 vertices;...

state is a particular case of a stabilizer state as well as a 2-uniform hypergraph state, a generalization where the edges have cardinality between 1 and...

Dhruv; Verstraëte, Jacques (2012), "The de Bruijn-Erdős Theorem for Hypergraphs", Des. Codes Cryptogr., 65 (3): 233–245, arXiv:1007.4150, doi:10.1007/s10623-011-9555-4...

multi-modal graphs[clarification needed], graphs with parallel edges, and hypergraphs. It provides a mechanism for annotating graphs, entities, and relations...

incidence geometry. In the latter case they are closely related to regular hypergraphs and biregular bipartite graphs, but with some additional restrictions:...

Ta Sheng (2018), "Improved bounds for the Graham-Pollak problem for hypergraphs", Electronic Journal of Combinatorics, 25 (1): Paper No. 1.4, arXiv:1708...

of these can be used to define a type of k {\displaystyle k} -regular hypergraph or a structure which is a generalisation of the line graph (the case when...

The game can be generalised even further by playing on an arbitrary hypergraph, where rows are hyperedges and cells are vertices. Other variations of...

Maximum-cardinality matching Perfect matching in high-degree hypergraphs Hall-type theorems for hypergraphs The unique perfect matching problem Alan Gibbons, Algorithmic...

object. Volume meshes may also be used for portal rendering. B-rep Voxels Hypergraph Volume rendering "Volume Mesh Generation for Numerical Flow Simulations...

S2CID 119297359. Meshulam, Roy (2001-01-01). "The Clique Complex and Hypergraph Matching". Combinatorica. 21 (1): 89–94. doi:10.1007/s004930170006. ISSN 1439-6912...

graphs, lexicographic product of graphs, series–parallel graphs. In a hypergraph, an edge can join any positive number of vertices. An undirected graph...

segmentation applications. As an extension of regular graph cuts, multi-level hypergraph cut is proposed to account for more complex high order correspondences...

Aykanat. His dissertation was published by the Bilkent University as Hypergraph Models for Sparse Matrix Partitioning and Reordering. Çatalyürek began...

directly to hypergraph coloring problems, where one requires that each hyperedge have vertices of more than one color. As for graphs, a hypergraph has a k...

problem, and indicated an iterative process using logical matrices and hypergraphs to obtain a solution. Look up schedule or scheduling in Wiktionary, the...

probabilistic combinatorics particularly for his result on independent sets in hypergraphs which found immediately several applications in additive number theory...

the graphics API, without any intermediary processing.[citation needed] Hypergraph Möller-Trumbore algorithm for ray-triangle intersection Nonobtuse mesh...

belonging to these cycles. Apply a triangle removal lemma for 3-uniform hypergraphs of high girth to show that, with high probability, the remaining points...

similar constructs such as, but not limited to, directed graphs and hypergraphs. Razborov, Alexander (December 2007). "Flag algebras" (PDF). The Journal...

Primal graph may refer to: Primal graph (hypergraphs) of a hypergraph A primal graph may be the planar graph from which a dual graph is formed Primal constraint...

every Reo program, called a connector or circuit, is a labeled directed hypergraph. Such a graph represents the data-flow among the processes in the system...

planes in Euclidean space. For every Levi graph, there is an equivalent hypergraph, and vice versa. The Desargues graph is the Levi graph of the Desargues...

(2019). "The average-case complexity of counting cliques in Erdős–Rényi hypergraphs". Proceedings of FOCS 2019. Carmosino, Marco L.; Gao, Jiawei; Impagliazzo...

Voss (1969) proved f(3) = 6 and 9 ≤ f(4) ≤ 12. A family F of graphs or hypergraphs is defined to have the Erdős–Pósa property if there exists a function...

{\displaystyle k} -map-hypergraph is a map-hypergraph that can be decomposed into k {\displaystyle k} edge-disjoint map-hypergraphs. Theorem. If G {\displaystyle...

Johnson's classical NP-complete problems. The problem is sometimes called hypergraph 2-colorability. The optimization version of this problem is called max...

K3 as their line graph. The Whitney graph theorem can be extended to hypergraphs. While graph isomorphism may be studied in a classical mathematical way...

theorem at the nLab Meshulam, Roy (2001-01-01). "The Clique Complex and Hypergraph Matching". Combinatorica. 21 (1): 89–94. doi:10.1007/s004930170006. ISSN 1439-6912...

combinations of its column vectors. In computational geometry, it refers to a hypergraph, a pair (X, R) where each r in R is a subset of X. This disambiguation...

Directed acyclic graph Propositional directed acyclic graph Multigraph Hypergraph Lightmap Winged edge Quad-edge Routing table Symbol table Piece table...

Hamiltonicity. Some of Chvátal's work concerns families of sets, or equivalently hypergraphs, a subject already occurring in his Ph.D. thesis, where he also studied...

br/ftp_pub/lfm/L1J_WindowViewport.pdf https://www.siggraph.org/education/materials/HyperGraph/viewing/view2d/2dview0.htm Archived 2016-03-03 at the Wayback Machine...

Kővári–Sós–Turán theorem to hypergraphs, as well as the supersaturation theorem, by creating a corresponding hypergraph for every graph that is K r (...

number of steps in the ordering between its two endpoints). Width of a hypergraph - the size of a smallest subset of edges that meets all other edges. %$WIDTH%...

the class of split graphs and for her contributions to line graphs of hypergraphs. In 1998, she was awarded the Belarus State Prize [be] for her book Lectures...

have been developed, and hyper-optimized contraction planners based on hypergraph partitioning brought orders-of-magnitude further speedups. These techniques...

relation and a graph a symmetric relation. For heterogeneous relations a hypergraph has edges possibly with more than two nodes, and can be illustrated by...

In the context of quantum mechanics and quantum information theory, symmetric, informationally complete, positive operator-valued measures (SIC-POVMs)...

However, in other areas of mathematics, simple games are also called hypergraphs or Boolean functions (logic functions). A simple game W is monotonic...

a hypergraph resembling the consistency constraint-structure of a database, a locking policy that visits entities along the paths of this hypergraph will...

research in block designs, projective planes, Intersection graphs of hypergraphs, and coding theory. He was a visiting professor at IIT Mumbai, University...

Paul M. (2012). Psychology Applied to Work. Summerfield, North Carolina: Hypergraph Press, Inc. Schaufeli, W. B., & Bakker, A. B. (2010), Defining and measuring...

Combinatorica, 1(1981), 169–197. József Beck's paper on the discrepancy of hypergraphs, awarded the 1985 Fulkerson Prize. J. Beck: Roth's estimate of the discrepancy...

Network", arXiv:1105.1697 [math.ST] Kovacs, E.; Szantai, T. (2012). "Hypergraphs in the characterization of regular-vine copula structures". Proc. 13th...

In computer science, a graph is an abstract data type that is meant to implement the undirected graph and directed graph concepts from the field of graph...

counting constraint satisfaction problems (#CSP). A #CSP instance is a hypergraph G=(V,E) called the constraint graph. Each hyperedge represents a variable...

graph formed from the vertices and edges of a geometric hypercube. hypergraph A hypergraph is a generalization of a graph in which each edge (called a hyperedge...

Most classes of CSPs that are known to be tractable are those where the hypergraph of constraints has bounded treewidth, or where the constraints have arbitrary...

generalised even further from the above variants by playing on an arbitrary hypergraph where rows are hyperedges and cells are vertices. Many board games share...

this setting can be shown using the hypergraph removal lemma, in the spirit of Solymosi's proof. The hypergraph removal lemma was shown independently...

N.; Harrison, P. G.; Knottenbelt, W. J. (2004). "Uniformization and hypergraph partitioning for the distributed computation of response time densities...

Subhash; Regev, Oded (2003), A new multilayered PCP and the hardness of hypergraph vertex cover, Association for Computing Machinery, pp. 595–601, doi:10...

In mathematics, a projective plane is a geometric structure that extends the concept of a plane. In the ordinary Euclidean plane, two lines typically intersect...

selection: Brouwer, Andries E., and Antoon WJ Kolen. "A super-balanced hypergraph has a nest point." Stichting Mathematisch Centrum. Zuivere Wiskunde ZW...

generalization of Hall's theorem to bipartite hypergraphs is provided by various Hall-type theorems for hypergraphs. Rado's theorem generalizes Hall's theorem...

various kinds of graphs, e.g., heterogeneous graphs, temporal graphs and hypergraphs. Moreover, numerous graph-related applications are found to be closely...

system are related (an adhesive category with coproducts is a HLR system). Hypergraph, typed graph and attributed graph rewriting, for example, can be handled...

various characterizations in terms of perfect elimination orderings, hypergraphs and matrices. They are closely related to strongly chordal graphs. By...

Evolution of Stories" and "HyperStorylines: Interactively untangling dynamic hypergraphs," with the latter article citing the former. The comics have featured...

ratio between the fractional matching number and the matching number in a hypergraph. Zoltán Füredi at the Mathematics Genealogy Project Füredi, Zoltán (1983)...

the vertices of the polytope. Enumerating the minimal transversals of a hypergraph. This problem is related to monotone dualization and is connected to many...

translation: Graphs and Hypergraphs, North-Holland Publishing Company, 1973. Hypergraphes. Combinatoires des ensembles finis (Hypergraphs. Combinatorial finite...

case the Erdős–Ko–Rado theorem and can be restated in terms of uniform hypergraphs. It is named after Joseph Kruskal and Gyula O. H. Katona, but has been...

problem. Given an instance of numeric 3d-matching, construct a tripartite hypergraph with sides X {\displaystyle X} , Y {\displaystyle Y} and Z {\displaystyle...

with Laura Florescu, American Mathematical Society, 2014. Packing in a hypergraph Joel Spencer at the Mathematics Genealogy Project "Putnam Competition...

isomorphism problem involves bipartite matching as a sub-problem. Matching in hypergraphs - a generalization of matching in graphs. Fractional matching. Dulmage–Mendelsohn...

Braß, Peter (2004), "Turán-type extremal problems for convex geometric hypergraphs", in Pach, János (ed.), Towards a theory of geometric graphs, Contemporary...

specific hypergraphs are known on which the strategy stops working. In all conditions, k is the size of winning-sets (i.e., the game hypergraph is k-uniform)...

Flaass, A. V. Kostochka, Zs. Tuza (1992). "Small transversals in uniform hypergraphs". Siberian Adv. Math. (in undetermined language). 2: 82–88.{{cite journal}}:...

(1990-10-15). "On a possible extension of Hall's theorem to bipartite hypergraphs". Discrete Mathematics. 84 (3): 309–313. doi:10.1016/0012-365X(90)90136-6...

Zaslavsky (1994) Oxley (1992), p. 26 Oxley (1992), p. 64 "The Matroids and Hypergraphs Packages in Maple 2024" (PDF). MapleSoft. Retrieved 2024-08-19. White...

set-family over the set of colors [n + 1]. This set-family can be seen as a hypergraph. If, for every vertex v on a face of the simplex, the colors in f(v) are...

many other combinatorial structures, such as sequences, tournaments, hypergraphs and graph limits. In general, the theory of quasi-randomness gives a...

news}}: CS1 maint: url-status (link) Sloman, Leila (July 14, 2022). "Hypergraphs reveal solution to 50-year-old problem". Quanta Magazine. Retrieved May...

Retrieved 2024-10-10. Bollobás, Béla (1986), Combinatorics: Set Systems, Hypergraphs, Families of Vectors, and Combinatorial Probability, Cambridge University...

regularity have also been studied, as well as extensions of regularity to hypergraphs. Applications of graph regularity often utilize forms of counting lemmas...

Erdős–Ko–Rado theorem can be described either in terms of set systems or hypergraphs. It gives an upper bound on the number of sets in a family of finite...

formulated as partitioning the hypergraph by cutting a minimal number of hyperedges. They make use of hMETIS which is a hypergraph partitioning package system...

problems, dynamic and online algorithms, and algorithms for graphs and hypergraphs. Ausiello was among the founders of the European Association for Theoretical...

structural property of queries that is defined with respect to the query's hypergraph: a conjunctive query is acyclic if and only if it has hypertree-width...

{\text{NP/poly}}} . The vertex cover problems in d {\displaystyle d} -uniform hypergraphs has kernels with O ( k d ) {\displaystyle O(k^{d})} edges using the sunflower...

1972, and D.Phil and MA in 1975. His doctoral dissertation, Matroids, Hypergraphs and the Max-Flow Min-Cut Theorem, was supervised by Aubrey William Ingleton...

players, Nash solvability in pure strategies is equivalent to duality of hypergraphs. For zero-sum games this was shown by J. Edmonds and D. R. Fulkerson...

anticipating the development of database management systems. Incidence structure Hypergraph Logic of relatives Logical matrix Partial order Predicate (mathematical...

Sciences, with a dissertation titled Paths and Cycles in Graphs and Hypergraphs under the advisement of László Lovász and András Recski. Since 2024 he...

MR 0302480. Lovász, László (1974), "Minimax theorems for hypergraphs", Hypergraph Seminar (Proc. First Working Sem., Ohio State Univ., Columbus,...

Annamalai, Chidambaram (2018), "Finding perfect matchings in bipartite hypergraphs", Combinatorica, 38 (6): 1285–1307, arXiv:1509.07007, doi:10.1007/s00493-017-3567-2...

1016/0012-365X(73)90108-8 Voloshin, Vitaly I. (2002), Coloring Mixed Hypergraphs: Theory, Algorithms and Applications., American Mathematical Society...

Zlatić, Vinko; Ghoshal, Gourab; Caldarelli, Guido (25 September 2009). "Hypergraph topological quantities for tagged social networks". Physical Review E...

refer to one of the following: Hypertree, a special kind of hypergraph, e.g., a hypergraph without cycles Hypertree decomposition in constraint satisfaction...

exponent √n for strongly regular graphs was done by Spielman (1996). For hypergraphs of bounded rank, a subexponential upper bound matching the case of graphs...

Spring 2016. Bryan Bischof. Higher order co-occurrence tensors for hypergraphs via face-splitting. Published 15 February 2020, Mathematics, Computer...

financial option pricing. Some problems in machine learning use graph- or hypergraph-based formulations having edges assigned with weights, most commonly positive...

(= vertices in the independent set). Similarly, when H is an r-partite hypergraph, Ψ ( L ( H ) ) ≥ ν ( H ) / r {\displaystyle \Psi (L(H))\geq \nu (H)/r}...

Weisstein, Eric W. "Turán Graph". MathWorld. Covering design data – Database of extremal hypergraphs and covering designs maintained by Klas Markström...

(2008). https://doi.org/10.1007/s00407-008-0025-y Duchet, Pierre (1995), "Hypergraphs", in Graham, R. L.; Grötschel, M.; Lovász, L. (eds.), Handbook of combinatorics...

Addison-Wesley. p. 236. ISBN 9780201530827. Eiter, Thomas; Gottlob, Georg (2002). "Hypergraph transversal computation and related problems in logic and AI". In Flesca...

(2012). "Efficient Dominating and Edge Dominating Sets for Graphs and Hypergraphs". Algorithms and Computation. Lecture Notes in Computer Science. Vol...

Természettudományi Értesítő, 34: 104–119. Lovász, László (1972a), "Normal hypergraphs and the perfect graph conjecture", Discrete Mathematics, 2 (3): 253–267...

approximated within a factor of d. This is also true for the weighted version. Hypergraph matching is equivalent to set packing: the sets correspond to the hyperedges...

Eiter, T.; Gottlob, G. (1995). "Identifying the Minimal Transversals of a Hypergraph and Related Problems". SIAM Journal on Computing. 24 (6): 1278. CiteSeerX 10...

linear program is 1/4. The implies a 1/4-approximation algorithm, using hypergraph matching. However, they could not prove that the algorithm converges in...

Bronnimann and Goodrich employed analogous methods to find set covers for hypergraphs with small VC dimension. In operations research and on-line statistical...

Springer. ISBN 0-387-18191-1. 2012 pbk reprint Packing in a hypergraph Frankl–Rödl graph Hypergraph removal lemma "Foreign Fellows of the Learned Society :...

by Jackson & Jordán (2005). Streinu, I.; Theran, L. (2009), "Sparse hypergraphs and pebble game algorithms", European Journal of Combinatorics, 30 (8):...

Pöschel, R. (1985), "On circle graphs", in Sachs, Horst (ed.), Graphs, Hypergraphs and Applications: Proceedings of the Conference on Graph Theory Held...

"Anti-Hadamard Matrices, Coin Weighing, Threshold Gates, and Indecomposable Hypergraphs". Journal of Combinatorial Theory, Series A. 79 (1): 133–160. doi:10...

tree-like data, structured graph-like data, data with inheritance, and hypergraph-like data. By relying on a non-standard data and query model, TypeDB (at...

Suzanne Renick; Dombrower, Micah; Goldberg, Debra S. (2014). "Using 2-node hypergraph clustering coefficients to analyze disease-gene networks". Proceedings...

case of Baranyai's theorem concerning the 1-factorization of complete hypergraphs. One method for constructing a 1-factorization of a complete graph on...

Graham is also cited as the co-inventor of the GYO algorithm to test if a hypergraph is acyclic. UC Berkeley EECS: In Memoriam "Martin H. Graham; EECS at UC...

of finding a maximum-cardinality matching in hypergraphs is NP-complete even for 3-uniform hypergraphs. West, Douglas Brent (1999), Introduction to Graph...

ISBN 978-0-521-79722-1, doi:10.1017/CBO9780511814068. Combinatorics - set systems, hypergraphs, families of vectors, and combinatorial probability. Cambridge University...

simplicial complex; A random k-dimensional simplicial complex; A random hypergraph; A random Čech complex. Hurewicz theorem relates the homological connectivity...

multivariate statistics Hinge theorem in geometry Hinge decomposition of hypergraphs, used when studying constraint satisfaction problems See Hinge (surname)...

1007/978-3-642-03735-1_3, ISBN 978-3-642-03734-4. Szántai, T.; Kovács, E. (2010), "Hypergraphs as a mean of discovering the dependence structure of a discrete multivariate...

sequences is nearly sharp", which introduced the notion of discrepancy on hypergraphs and established an upper bound on the discrepancy of the family of arithmetic...

for Circuit partitioning: high-performance heuristic optimizations for hypergraph partitioning Placement: algorithms for finding ( x , y ) {\displaystyle...

doi:10.1145/2157.322404. Saccà, Domenico (1986). "Closures of Database Hypergraphs". Journal of the ACM. 32 (4): 774–803. doi:10.1145/4221.4997. Saccà,...

When IC designs grew to millions of components, placement leveraged hypergraph partitioning using nested-partitioning frameworks such as Capo. Combinatorial...

geometric hypergraphs", Discrete and Computational Geometry, 19 (4): 473–484, doi:10.1007/PL00009365 Suk, Andrew (2013), "A note on geometric 3-hypergraphs",...

× 293. It is a candidate Lychrel seed number. There are 879 regular hypergraphs spanning 4 vertices. 880 = 24 × 5 × 11 = 11!!!. It is a Harshad number...

sets behave pseudorandomly, in the sense that corresponding graphs and hypergraphs have the correct subgraph densities for some fixed set of small (hyper)subgraphs...

be the primal treewidth, dual treewidth, or incidence treewidth of the hypergraph associated to the SAT formula, whose vertices are the variables and where...

a collection of subsets of ⁠ V {\displaystyle V} ⁠, is also called a hypergraph. When using this terminology, the elements in the set ⁠ V {\displaystyle...

She was one of the authors of the GYO algorithm to test acyclicity of hypergraphs. She joined the faculty at Case Western Reserve University in 1980, becoming...

conveyed by the natural language is represented sentence by sentence as a hypergraph composed of a set of directed binary labeled links between nodes or hypernodes...

vertices, possibly held in index buffers. describes geometry as a graph or hypergraph. CSG Constructive solid geometry, a method for generating complex solid...

supervision of Harvey Abbott, with the dissertation Some Results on Hypergraphs. He also received a professional diploma in education alongside his doctorate...

Borndörfer, Ralf (2018-10-01). "Hall's and Kőnig's theorem in graphs and hypergraphs". Discrete Mathematics. 341 (10): 2753–2761. doi:10.1016/j.disc.2018...

methods for heterophily on heterogeneous graphs, temporal graphs and hypergraphs are still under-explored. Diffusion of innovations § Heterophily and...

for LOGCFL include many problems that can be characterized by acyclic hypergraphs: evaluating acyclic Boolean conjunctive queries checking the existence...

Numbers, Academic Press, ISBN 9780122091308 Duchet, Pierre (1995), "Hypergraphs", in Graham, R. L.; Grötschel, M.; Lovász, L. (eds.), Handbook of combinatorics...

is modeled as a hypergraph. Partitioning this hypergraph is essential for optimal resource allocation and minimizing wiring. Hypergraph coarsening helps...

Wormald (1983). Burr, Stefan A. (1980), "Subtrees of directed graphs and hypergraphs", Proceedings of the Eleventh Southeastern Conference on Combinatorics...

modules and nets are interpreted as forming the nodes and hyperedges of a hypergraph then the graph formed from them is its line graph. An interval representation...

algorithm Strongly connected component Vertex cover problem See list of network theory topics Helly family Intersection (Line) Graphs of hypergraphs...

of 1-matching polyhedra", in Berge, C.; Ray-Chaudhuri, D. K. (eds.), Hypergraph Seminar, Lecture Notes in Mathematics, vol. 411, Springer-Verlag, pp. 214–242...

mathematics, completing her Ph.D. in 1999. Her dissertation, Graphs and Hypergraphs as Interconnection Network Models, was supervised by Carles Padró Laimón...

MR 0288823. Buzaglo, Sarit; Pinchasi, Rom; Rote, Günter (2013), "Topological hypergraphs", in Pach, János (ed.), Thirty Essays on Geometric Graph Theory, Springer...

digraphs, see new digraph reconstruction conjecture. Hypergraphs, including all k-uniform hypergraphs for k>2 (Kocay). Infinite graphs. If T is the tree...

collaboration graph of mathematicians have also been considered. There is a hypergraph version, where individual mathematicians are vertices and where a group...

Bruno; Engelfriet, Joost; Rozenberg, Grzegorz (1993), "Handle-rewriting hypergraph grammars", Journal of Computer and System Sciences, 46 (2): 218–270, doi:10...

Farber, Martin; Jamison, Robert E. (1986), "Convexity in graphs and hypergraphs", SIAM Journal on Algebraic and Discrete Methods, 7 (3): 433–444, doi:10...

Hamiltonian graphs directed graphs and tournaments and to k-uniform hypergraphs. have been characterized. The frequency partitions of the following families...

fixed angle Nathan Keller and Noam Lifshitz for The junta method for hypergraphs and the Erdős–Chvátal simplex conjecture Source: American Mathematical...

András (1985), "Chromatic number of finite and infinite graphs and hypergraphs" (PDF), Discrete Mathematics, 53: 281–285, doi:10.1016/0012-365X(85)90148-7...

(mathematical analysis) Strong perfect graph theorem (graph theory) Symmetric hypergraph theorem (graph theory) Szemerédi's theorem (combinatorics) Theorem on...

master's degree in 1992 and completing her Ph.D. in 1998. Her dissertation, Hypergraphs and Automorphic Forms, was supervised by James Arthur, a specialist on...

paper with Erdős on graph coloring problems for infinite graphs and hypergraphs. This paper extends greedy coloring methods from finite to infinite graphs:...

sketch operations, A popular Natural Language Processing models, and hypergraph models of similarity, Generalized linear array model in statistics Two-...

their low autocorrelation properties. Binary sequence Discrepancy of hypergraphs Rudin–Shapiro sequence Konev, Boris; Lisitsa, Alexei (2014). "A SAT attack...

Helly family Hypergeometric function identities Hypergeometric series Hypergraph Incidence structure Induction puzzles Integer partition Ferrers graph...

represented by a graph, while forms with k-edges can only be related by hypergraphs. A k-edge can be seen as a set of vertices, with no order implied. They...

111–120, doi:10.1142/S0129054196000099. Lovász, László (1972), "Normal hypergraphs and the perfect graph conjecture", Discrete Mathematics, 2 (3): 253–267...

In quantum information theory, a set of bases in Hilbert space Cd are said to be mutually unbiased if when a system is prepared in an eigenstate of one...

Combinatorial mathematics, IX (Brisbane, 1981), LNM Some NP-complete problems for hypergraph degree sequences, CJ Colbourn, WL Kocay, DR Stinson – Discrete Applied...

reflecting telescope, featuring a primary mirror of 400 mm diameter (16″ f/8 Hypergraph) and a computer aided mount of type Knopf MK70S were first used during...

Fizikai Lapok (in Hungarian), 38: 116–119 Lovász, László (1972a), "Normal hypergraphs and the perfect graph conjecture", Discrete Mathematics, 2 (3): 253–267...

published many results in combinatorics, particularly in extremal graph and hypergraph theory and Ramsey Theory. In joint work with Tom Bohman he established...

1002/mana.19600220107. MR 0121311.. Berge, Claude (1973). Graphs and Hypergraphs. North-Holland Publishing Company. pp. 169–170. ISBN 0-444-10399-6. Berge...

Pöschel, R. (1985), "On circle graphs", in Sachs, Horst (ed.), Graphs, Hypergraphs and Applications: Proceedings of the Conference on Graph Theory Held...

parameter |citeseerx= (help). Barthélémy, Jean-Pierre (1989), "From copair hypergraphs to median graphs with latent vertices", Discrete Mathematics, 76 (1):...

MathSciNet (AMS). Bollobás, Béla (1986). Combinatorics: Set systems, hypergraphs, families of vectors and combinatorial probability. Cambridge: Cambridge...

Copies of the Mandelbrot Set: I Robert Morris 2017 Independent sets in Hypergraphs Umberto Hryniewicz and Pedro Salomão 2015 A Poincaré-Birkhoff theorem...

Skupień, Z. (1989), "Exponentially many hypohamiltonian graphs", Graphs, Hypergraphs and Matroids III (Proc. Conf. Kalsk 1988), Zielona Góra: Higher College...

he was given a grant for "Approximate structure in large graphs and hypergraphs." With an education stemming back From the late 90's and early 2000's...

with Richard Giles, and the terms clutter and blocker in the study of hypergraphs. A recurring theme in his work is to seek algorithms whose time complexity...

and R be a set of subsets of X; such a pair is called a range space or hypergraph, and the elements of R are called ranges or hyperedges. An ε-net of a...

S2CID 14422769. M. Rossi; M. Huber; D. Bruß; C. Macchiavello (2013). "Quantum Hypergraph States". New Journal of Physics. 15 (11) 113022. arXiv:1211.5554. Bibcode:2013NJPh...

ISBN 978-3-642-27874-7, MR 2920058 Streinu, I.; Theran, L. (2009), "Sparse hypergraphs and pebble game algorithms", European Journal of Combinatorics, 30 (8):...

\\3&8\end{smallmatrix}}\right]} Its structure can be represented as a hypergraph, connecting 8 nodes by 8 3-node-set hyperedges. It has a real representation...

be proved by reduction from the problem of 3-dimensional matching in a hypergraph). Abraham, Blum and Sandholm present two techniques for maximum cycle...

a graph database. These represent entities as the nodes of a graph or hypergraph, and attributes as links or edges of that graph. The issue of table joins...

"Anti-Hadamard Matrices, Coin Weighing, Threshold Gates, and Indecomposable Hypergraphs". Journal of Combinatorial Theory, Series A. 79 (1): 133–160. doi:10...

w_{2,3}=1,w_{1}=1} . In hypergraph terminology, a collection B is balanced with respect to its ground-set V, iff the hypergraph with vertex-set V and edge-set...

something written at the end of a document (for example, a postscript) Hypergraph, in mathematics Hypographa, a genus of moths Hypographia, another, obsolete...

establish a scientific analogy between spider silk and musical composition. Hypergraph Modeling language Ontology language Operad theory Orgology Universal algebra...

S2CID 31590247. Damavandi, Ojan Khatib; Robert M. Ziff (2015). "Percolation on hypergraphs with four-edges". J. Phys. A: Math. Theor. 48 (40) 405004. arXiv:1506...

original on 2006-10-12. Retrieved 2006-12-29. Radiosity Overview, from HyperGraph of SIGGRAPH Archived 2011-09-27 at the Wayback Machine (provides full...

sketch operations, in a popular Natural Language Processing models, and hypergraph models of similarity. The Face-splitting product and his properties used...

formalized the STP with an iterative algorithm using logical matrices and hypergraphs. Nelishia Pillay published a comprehensive survey paper of these algorithms...

Beck gives a winning condition for Maker. It uses the pair-degree of the hypergraph - denoted by d 2 {\displaystyle d_{2}} . This condition can be generalized...

2014, pp. 1003–1006. Arxiv with Morris, Samotij: Independent sets in hypergraphs, J. AMS, vol. 28, 2015, pp. 669–709, Arxiv 2012 with Hong Liu, Maryam...

) ( x ) {\displaystyle h_{D(x)}(x)} . Stefan, Walzer (2020). Random hypergraphs for hashing-based data structures (PhD). pp. 27–30. Dietzfelbinger, Martin;...

2-element subsets are faces of K, is itself a face of K. 3. Let H be a hypergraph. A matching in H is a set of edges of H, in which every two edges are...

Farber, Martin; Jamison, Robert E. (1986), "Convexity in graphs and hypergraphs", SIAM Journal on Algebraic and Discrete Methods, 7 (3): 433–444, doi:10...

ISBN 0-387-05889-3 Bollobás, Béla (1986). Combinatorics: set systems, hypergraphs, families of vectors, and combinatorial probability. Cambridge University...

 287–293. Tuza, Zsolt (1988). Extremal problems on saturated graphs and hypergraphs. Eleventh British Combinatorial Conference (London, 1987). Ars Combinatoria...

over slim three-dimensional tables, the settling of the complexity of hypergraph degree sequences, and the introduction of colorful linear programming...

Frank, András (1976), "Some polynomial algorithms for certain graphs and hypergraphs", Congressus Numerantium, XV: 211–226. Füredi, Zoltán (1987), "The number...

104, MR 2392060, S2CID 2826. Streinu, I.; Theran, L. (2009), "Sparse hypergraphs and pebble game algorithms", European Journal of Combinatorics, 30 (8):...

277. Nagle, Brendan; Rödl, Vojtěch; Schacht, Mathias (2006), "Extremal hypergraph problems and the regularity method", in Klazar, Martin; Kratochvíl, Jan;...

Random trial formulation: Randomized controlled trial Discrepancy of hypergraphs Geometric discrepancy theory Weyl, Hermann (1 September 1916). "Über...

 60, ISBN 0-387-24219-8, MR 2127991. Lovász, László (1972), "Normal hypergraphs and the perfect graph conjecture", Discrete Mathematics, 2 (3): 253–267...

Laekhanukit and Nanongkai prove approximation hardness to a variant called k-hypergraph pricing. They also prove hardness for unit-demand min-buying and single-minded...

value of a function on graphs when evaluated on sparse random graphs and hypergraphs, since in a sparse random graph, it is much more likely for any particular...

flows, matchings; B. Matroids, trees, stable sets; C. Disjoint paths, hypergraphs) Discrete and Computational Geometry: The Goodman-Pollack Festschrift...

the nature of embeddings of large sparse graphs into dense graphs. A hypergraph variant was developed later by Peter Keevash. He is member of the editorial...

need to be familiar with, or comfortable looking up, terminology for hypergraphs and metric spaces. He suggests that the appropriate audience for the...

Univ. Press, pp. 153–171, MR 2187738. Lovász, László (1972a), "Normal hypergraphs and the perfect graph conjecture", Discrete Mathematics, 2 (3): 253–267...

ISBN 978-3-540-89549-7, MR 2672388. Lovász, László (1972), "Normal hypergraphs and the perfect graph conjecture", Discrete Mathematics, 2 (3): 253–267...

the order 2 biplane (a symmetric (7,4,2)-design). Algebraic statistics Hypergraph Williamson conjecture Stinson 2003, pg.1 Hayashi, Takao (2008). "Magic...

result. Cell (biology) Biologically inspired computing Formal language Hypergraph MGS Systems biology Păun, Gheorghe (1998). Computing with Membranes. TUCS...

enumeration and random graphs, the sixth generalizes from graphs to hypergraphs, and the seventh concerns infinite graphs. The book concludes with a...

Inc., pp. 109–110, ISBN 81-7808-830-4. Berge, Claude (1973), Graphs and Hypergraphs, North-Holland Publishing Company, pp. 122–125, ISBN 0-444-10399-6....

the sharp threshold for the existence of a perfect matching in a random hypergraph. Solution to the Deligne-Lusztig Theory: a way of constructing linear...

algebraic and combinatorial properties of edge ideals of graphs and hypergraphs. Her work is published in the Journal of Pure and Applied Algebra, the...

the sharp threshold for the existence of a perfect matching in a random hypergraph. In 2010, Terence Tao and Vu solved the circular law conjecture in random...

this case a clique graph is best thought of a particular example of a hypergraph. The Erdős–Rényi model shows a series of interesting transitions when...

Bednarska-Bzdęga, Małgorzata (2014-01-12). "Avoider-Forcer Games on Hypergraphs with Small Rank". The Electronic Journal of Combinatorics. 21 (1): 1–2...

Initially, most of his research themes had as their main subject graphs, hypergraphs and matroids, and were linked to famous and difficult problems in Graph...

generating a hypergraph. Then, the size of the graph is reduced with respect to the constraints. First, the existence of substructures in the hypergraph is checked...

436–452. de Caen, D. (1994). "The current status of Turán's problem on hypergraphs". In Frankl, P.; Füredi, Z.; Katona, G.; Miklós, D. (eds.). Extremal...

ISBN 9789048194162. Pasch's theorem Pasch's axiom Pasch configuration Pasch hypergraph Ordered geometry Dirk Schlimm, "The correspondence between Moritz Pasch...

point of view of graph grammars, term graphs are not regular graphs, but hypergraphs where an n-ary word will have a particular subgraph in first place, another...

Anthony; Rajapakse, Indika (2024-04-10), Kronecker Product of Tensors and Hypergraphs: Structure and Dynamics, arXiv:2305.03875 Leonardo, Colombo; Manuel,...

higher-order networks, such as multiplex networks, temporal networks and hypergraphs. Lambiotte has made contributions to the field of social network analysis...

Fundamenta Mathematicae. 23: 135–142. Haim Hanani (1979). "Decomposition of Hypergraphs into Octahedra". Transactions of the New York Academy of Sciences. 319...

(2006), "Finding and counting cliques and independent sets in r-uniform hypergraphs", Information Processing Letters, 99 (4): 130–134, doi:10.1016/j.ipl...

A frequently used tool in his papers is tree structure of graphs and hypergraphs such as for hypertrees, strongly chordal graphs and chordal graphs. He...

combinatorial techniques. Often, the input to a positional game is considered a hypergraph. In this case: The elements of X {\displaystyle X} are called vertices...

edge coloring of a countably infinite complete graph or complete uniform hypergraph, using finitely many colors, contains a monochromatic infinite induced...

Jean-Daniel (1 January 2021). "Analyzing Dynamic Hypergraphs with Parallel Aggregated Ordered Hypergraph Visualization". IEEE Transactions on Visualization...

Extremal Graph-Theory (with Erdős Pál, 1982) Supersaturated Graphs and Hypergraphs (with Erdős Pál, 1983) On Restricted Colorings of K_n (with T. Sós Vera...

Magazine 74, #1 (February 2001), pp. 41–47. On the symmetry groups of hypergraphs of perfect cwatsets, Daniel K. Biss, Ars Combinatorica 56 (2000), pp...

transformation systems, or graph visualization tools. GXL includes support for hypergraphs and hierarchical graphs, and can be extended to support other types of...

levels of up to 95% have been obtained for complex biological networks. Hypergraphs are a generalization of graphs in which edges are not just couples of...

reduction from 3-satisfiability and also by a different reduction from hypergraph 2-coloring. However, it can easily be solved when all unordered triples...

deterministic. Peter Keevash found a generalization of the blow-up lemma to hypergraphs in 2010. Stefan Glock and Felix Joos discovered a variant of the blow-up...

József; Morris, Robert; Samotij, Wojciech (2015). "Independent sets in hypergraphs" (PDF). Journal of the American Mathematical Society. 28 (3): 669–709...

(2000). "Counting pattern-free set partitions II: Noncrossing and other hypergraphs". The Electronic Journal of Combinatorics. 7 (1): 25 pp. doi:10.37236/1512...

1007/s00493-003-0031-2. S2CID 20035419. Chvátal, V. (1974). Unsolved Problem No. 7. Hypergraph Seminar (Proc. First Working Sem., Ohio State Univ., Columbus, Ohio, 1972)...

 132–135, ISBN 0-12-289260-7, MR 0562306. Lovász, László (1972), "Normal hypergraphs and the perfect graph conjecture", Discrete Mathematics, 2 (3): 253–267...

chessboard. Equivalently, it is the set of matchings in a complete k-partite hypergraph. This complex is at least ( ν − 2 ) {\displaystyle (\nu -2)} -connected...

1016/0097-3165(94)90064-7 P. Erdős, L. Lovász, "Problems and results on 3-chromatic hypergraphs and some related questions", in A. Hajnal, R. Rado, and V. T. Sós, eds...

as a map, an arbitrary dessin is a hypermap: that is, a drawing of a hypergraph in which the black points represent vertices and the white points represent...

Bryant, David; Tupper, Paul (2014). "Diversities and the geometry of hypergraphs". Discrete Mathematics and Theoretical Computer Science. 16 (2): 1–20...

Amer. Math. Soc. Transl., 38: 206–212 Berge, Claude (1973), Graphs and Hypergraphs, Amsterdam: North-Holland Favaron, Odile (1988), "Two relations between...

They also showed that a similar algorithm could be used to find densest hypergraphs. There are many variations on the densest subgraph problem. One of them...

laboratory of Cambridge for her Ph.D. Her 2004 dissertation, Large Random Hypergraphs, was supervised by James R. Norris. She did postdoctoral research with...

MR 2004404. S2CID 5226655. Zbl 1028.05035. Lovász, László (1972). "Normal hypergraphs and the perfect graph conjecture". Discrete Mathematics. 2 (3): 253–267...

exactly one vertex in D {\displaystyle D} . The concept also extends to hypergraphs, where similar complexity results have been established. Bange, D.W.;...

József; Morris, Robert; Samotij, Wojciech (2015), "Independent sets in hypergraphs", Journal of the American Mathematical Society, 28 (3): 669–709, arXiv:1204...