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...

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

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...

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

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...

1908. Property B is equivalent to 2-coloring the hypergraph described by the collection C. A hypergraph with property B is also called 2-colorable.: 468 ...

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...

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

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...

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...

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

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

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

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...

graphs, simplicial complexes, cell complexes, combinatorial complexes and hypergraphs. Given a finite set S of abstract entities, a neighborhood function N...

application domains, with the input family of sets often being described as a hypergraph. A fundamental question in the study of SDR is whether or not an SDR exists...

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

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...

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...

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...

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

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...

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...

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

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

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...

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...