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...

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...

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, 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...

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

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

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...

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

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...

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

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...

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

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

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...

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....

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...

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

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...

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...

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...

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...

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...

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

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...

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

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

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...

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...