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D INTERVAL-HYPERGRAPH

D-interval hypergraph

Hypergraph representing intervals on real number lines

d-interval hypergraph is a kind of a hypergraph constructed using intervals of real lines. The parameter d is a positive integer. The vertices of a d-interval

D-interval hypergraph

D-interval_hypergraph

Matching in hypergraphs

Set of hyperedges where every pair is disjoint

hypergraph matching to 3-uniform hypergraphs. Vertex cover in hypergraphs Bipartite hypergraph Rainbow matching in hypergraphs D-interval hypergraph -

Matching in hypergraphs

Matching_in_hypergraphs

Packing in a hypergraph

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

Packing in a hypergraph

Packing_in_a_hypergraph

Helly family

Family of sets where every disjoint subfamily has k or fewer sets

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

Helly family

Helly_family

Discrepancy of hypergraphs

Area of discrepancy theory

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

Discrepancy of hypergraphs

Discrepancy_of_hypergraphs

Dually chordal graph

Graph whose maximal clique hypergraph is a hypertree

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

Dually chordal graph

Dually_chordal_graph

List of graph theory topics

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

List of graph theory topics

List_of_graph_theory_topics

List of NP-complete problems

Modularity maximization Monochromatic triangle Pathwidth, or, equivalently, interval thickness, and vertex separation number Rank coloring k-Chinese postman

List of NP-complete problems

List_of_NP-complete_problems

Glossary of graph theory

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

Glossary_of_graph_theory

List of data structures

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

List_of_data_structures

Independent set (graph theory)

Unrelated vertices in graphs

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

Independent set (graph theory)

Independent_set_(graph_theory)

Ε-net (computational geometry)

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

Ε-net (computational geometry)

Ε-net_(computational_geometry)

Reconstruction conjecture

Conjecture in graph theory

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

Reconstruction conjecture

Reconstruction_conjecture

NP-intermediate

Complexity class of problems

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

NP-intermediate

Forbidden subgraph problem

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

Forbidden subgraph problem

Forbidden_subgraph_problem

N-sphere

Generalized sphere of dimension n (mathematics)

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

N-sphere

Quantum contextuality

Context dependence in quantum measurements

of that kind. A more refined framework based on hypergraphs rather than graphs is also used. In the CbD approach, developed by Ehtibar Dzhafarov, Janne

Quantum contextuality

Quantum_contextuality

Pathwidth

Representation of a graph as a path graph "thickened" by some amount

forming the nodes and hyperedges of a hypergraph then the graph formed from them is its line graph. An interval representation of a supergraph of this

Pathwidth

Antoon Kolen

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

Antoon Kolen

Antoon_Kolen

Efficient dominating set

Mathematical concept in graph theory

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

Efficient dominating set

Efficient_dominating_set

Circle graph

Intersection graph of a chord diagram

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

Circle graph

Circle_graph

Perfect graph

Graph with tight clique-coloring relation

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

Perfect graph

Perfect_graph

Dilworth's theorem

On chains and antichains in partial orders

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

Dilworth's theorem

Dilworth's_theorem

Sperner's lemma

Theorem on triangulation graph colorings

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

Sperner's lemma

Sperner's_lemma

Graph isomorphism problem

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

Graph_isomorphism_problem

Maximal independent set

Independent set which is not a subset of any other independent set

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

Maximal independent set

Maximal_independent_set

Radiosity (computer graphics)

Computer graphics rendering method using diffuse reflection

surface per discrete time interval and is the combination of emitted and reflected energy: B ( x ) d A = E ( x ) d A + ρ ( x ) d A ∫ S B ( x ′ ) 1 π r 2

Radiosity (computer graphics)

Radiosity_(computer_graphics)

Vine copula

Graphical tool in probability

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

Vine copula

Vine_copula

Chromatic polynomial

Function in algebraic graph theory

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

Chromatic polynomial

Chromatic_polynomial

Mathematics

Field of knowledge

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

Mathematics

Antimatroid

Mathematical system of orderings or sets

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

Antimatroid

Dense subgraph

Highly connected subgraph

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

Dense subgraph

Dense_subgraph

Graph theory

Area of discrete mathematics

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

Graph theory

Graph_theory

Consensus clustering

Method of result aggregation from multiple clustering algorithms

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

Consensus clustering

Consensus_clustering

Chinese remainder theorem

About simultaneous modular congruences

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

Chinese remainder theorem

Chinese_remainder_theorem

Clique problem

Task of computing complete subgraphs

independent sets in r-uniform hypergraphs", Information Processing Letters, 99 (4): 130–134, doi:10.1016/j.ipl.2006.04.005. Zuckerman, D. (2006), "Linear degree

Clique problem

Clique_problem

Percolation threshold

Threshold of percolation theory models

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

Percolation threshold

Percolation_threshold

Knaster–Kuratowski–Mazurkiewicz lemma

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

Knaster–Kuratowski–Mazurkiewicz lemma

Knaster–Kuratowski–Mazurkiewicz_lemma

Median graph

Graph with a median for each three vertices

between them is called their distance, denoted by d ( x , y ) {\displaystyle d(x,y)} . The interval of vertices that lie on shortest paths between a {\displaystyle

Median graph