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...

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...

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

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...

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...

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....

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

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

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...

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

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 ...

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...

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...

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

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

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

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...

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...

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

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...

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...

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...

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

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

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

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...