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graph theory, a balanced hypergraph is a hypergraph that has several properties analogous to that of a bipartite graph. Balanced hypergraphs were introduced
Balanced_hypergraph
Generalization of graph theory
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
Hypergraph
Set of hyperedges where every pair is disjoint
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
Matching_in_hypergraphs
Generalizations in graph theory
theory, Hall-type theorems for hypergraphs are several generalizations of Hall's marriage theorem from graphs to hypergraphs. Such theorems were proved by
Hall-type theorems for hypergraphs
Hall-type_theorems_for_hypergraphs
In graph theory, the term bipartite hypergraph describes several related classes of hypergraphs, all of which are natural generalizations of a bipartite
Bipartite_hypergraph
Method in combinatorics
The method of (hypergraph) containers is a powerful tool that can help characterize the typical structure and/or answer extremal questions about families
Container_method
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
Truncated_projective_plane
a selection: Brouwer, Andries E., and Antoon WJ Kolen. "A super-balanced hypergraph has a nest point." Stichting Mathematisch Centrum. Zuivere Wiskunde
Antoon_Kolen
Subdivision of vertices into disjoint sets
as Zoltan by Devine et al. focus on hypergraph partitioning. Andreev, Konstantin; Räcke, Harald (2004). "Balanced graph partitioning". Proceedings of
Graph_partition
Graph divided into two independent sets
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
Bipartite_graph
Form taken by the network of interconnections of a circuit
hypergraph, the tentacles carry labels which are determined by the hyperedge's label. A conventional directed graph can be thought of as a hypergraph
Circuit_topology_(electrical)
Matrix that shows the relationship between two classes of objects
contrast, a hypergraph can have multiple vertices assigned to one edge; thus, a general matrix of non-negative integers describes a hypergraph. The incidence
Incidence_matrix
networks Fractional stable paths problems Fractional hypergraph matching (see also the NP-complete Hypergraph matching) Fractional strong kernel Scarf's lemma
List of PPAD-complete problems
List_of_PPAD-complete_problems
Symmetric arrangement of finite sets
the order 2 biplane (a symmetric (7,4,2)-design). Algebraic statistics Hypergraph Williamson conjecture Stinson 2003, pg.1 Hayashi, Takao (2008). "Magic
Combinatorial_design
relationship between chordal bipartite graphs and totally balanced neighborhood hypergraphs of bipartite graphs. A characterization of chordal bipartite
Chordal_bipartite_graph
2}, {2,3}, {1}} is balanced: choose w 1 , 2 = 0 , w 2 , 3 = 1 , w 1 = 1 {\displaystyle w_{1,2}=0,w_{2,3}=1,w_{1}=1} . In hypergraph terminology, a collection
Knaster–Kuratowski–Mazurkiewicz lemma
Knaster–Kuratowski–Mazurkiewicz_lemma
Data organization and storage formats
Directed acyclic graph Propositional directed acyclic graph Multigraph Hypergraph Lightmap Winged edge Quad-edge Routing table Symbol table Piece table
List_of_data_structures
Award for advancements in discrete mathematics
fixed angle Nathan Keller and Noam Lifshitz for The junta method for hypergraphs and the Erdős–Chvátal simplex conjecture Source: American Mathematical
Fulkerson_Prize
Abstract data type in computer science
adjacent vertices in more efficient data structures, such as hash tables or balanced binary search trees (the latter representation requires that vertices are
Graph_(abstract_data_type)
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
Glossary_of_graph_theory
products of graphs Walescki's theorem for hypergraphs: Do complete k {\displaystyle k} -uniform hypergraphs admit Hamiltonian decompositions into tight
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Theorem on triangulation graph colorings
a balanced labeling – a labeling in which the corresponding hypergraph admits a perfect fractional matching. To illustrate, here are some balanced labeling
Sperner's_lemma
Perfect graphs have neither odd holes nor odd antiholes
Természettudományi Értesítő, 34: 104–119. Lovász, László (1972a), "Normal hypergraphs and the perfect graph conjecture", Discrete Mathematics, 2 (3): 253–267
Strong_perfect_graph_theorem
Points and lines with equal incidences
incidence geometry. In the latter case they are closely related to regular hypergraphs and biregular bipartite graphs, but with some additional restrictions:
Configuration_(geometry)
Balanced complete multipartite graph
Weisstein, Eric W. "Turán Graph". MathWorld. Covering design data – Database of extremal hypergraphs and covering designs maintained by Klas Markström
Turán_graph
Braß, Peter (2004), "Turán-type extremal problems for convex geometric hypergraphs", in Pach, János (ed.), Towards a theory of geometric graphs, Contemporary
Tripod_packing
Unsolved problem in computational complexity theory
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
Graph_isomorphism_problem
Natural number
× 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
800_(number)
Israeli mathematician
Fundamenta Mathematicae. 23: 135–142. Haim Hanani (1979). "Decomposition of Hypergraphs into Octahedra". Transactions of the New York Academy of Sciences. 319
Haim_Hanani
Game where groups of players may enforce cooperative behaviour
However, in other areas of mathematics, simple games are also called hypergraphs or Boolean functions (logic functions). A simple game W is monotonic
Cooperative_game_theory
American mathematician and physics professor
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)
Hunter_Snevily
ISBN 978-3-540-89549-7, MR 2672388. Lovász, László (1972), "Normal hypergraphs and the perfect graph conjecture", Discrete Mathematics, 2 (3): 253–267
Skew_partition
Helly family Hypergeometric function identities Hypergeometric series Hypergraph Incidence structure Induction puzzles Integer partition Ferrers graph
Index of combinatorics articles
Index_of_combinatorics_articles
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