In the mathematical discipline of graph theory, a matching or independent edge set in an undirected graph is a set of edges without common vertices. In...
23 KB (2,938 words) - 07:47, 18 July 2024
In graph theory, a perfect matching in a graph is a matching that covers every vertex of the graph. More formally, given a graph G = (V, E), a perfect...
6 KB (785 words) - 09:05, 19 June 2023
mathematical area of graph theory, Kőnig's theorem, proved by Dénes Kőnig (1931), describes an equivalence between the maximum matching problem and the minimum...
24 KB (3,433 words) - 00:05, 30 April 2024
Maximum cardinality matching is a fundamental problem in graph theory. We are given a graph G, and the goal is to find a matching containing as many edges...
10 KB (1,317 words) - 19:11, 16 July 2024
Graph matching is the problem of finding a similarity between graphs. Graphs are commonly used to encode structural information in many fields, including...
3 KB (371 words) - 05:29, 3 January 2024
computer science and graph theory, the maximum weight matching problem is the problem of finding, in a weighted graph, a matching in which the sum of weights...
2 KB (231 words) - 22:59, 21 April 2024
bipartite graph Disperser Expander Extractor Bivariegated graph Cage (graph theory) Cayley graph Circle graph Clique graph Cograph Common graph Complement...
7 KB (664 words) - 12:10, 30 October 2023
Appendix:Glossary of graph theory in Wiktionary, the free dictionary. This is a glossary of graph theory. Graph theory is the study of graphs, systems of nodes...
107 KB (15,784 words) - 17:42, 20 August 2024
mathematical discipline of graph theory, a 3-dimensional matching is a generalization of bipartite matching (also known as 2-dimensional matching) to 3-partite hypergraphs...
13 KB (1,551 words) - 12:33, 12 August 2024
In the mathematical field of graph theory, a bipartite graph (or bigraph) is a graph whose vertices can be divided into two disjoint and independent sets...
33 KB (4,093 words) - 05:52, 26 August 2024
In graph theory, the hypercube graph Qn is the graph formed from the vertices and edges of an n-dimensional hypercube. For instance, the cube graph Q3...
13 KB (1,555 words) - 14:39, 18 September 2023
is known as the exact graph matching. In November 2015, László Babai announced a quasi-polynomial time algorithm for all graphs, that is, one with running...
40 KB (4,094 words) - 05:17, 2 August 2024
Assignment problem (category Matching (graph theory))
describing the problem using graph theory: The assignment problem consists of finding, in a weighted bipartite graph, a matching of a given size, in which...
16 KB (2,534 words) - 11:41, 29 July 2024
Hall's marriage theorem (redirect from Hall's perfect matching theorem)
number of sets in the group. The graph theoretic formulation answers whether a finite bipartite graph has a perfect matching—that is, a way to match each...
21 KB (3,208 words) - 06:26, 15 June 2024
Blossom algorithm (redirect from Edmonds's matching algorithm)
In graph theory, the blossom algorithm is an algorithm for constructing maximum matchings on graphs. The algorithm was developed by Jack Edmonds in 1961...
17 KB (2,022 words) - 19:16, 27 November 2023
Petersen's theorem (category Matching (graph theory))
Petersen's Theorem. Every cubic, bridgeless graph contains a perfect matching. In other words, if a graph has exactly three edges at each vertex, and...
13 KB (1,448 words) - 15:50, 4 June 2024
economics Nash bargaining game Matching (graph theory) Optimal matching Pissarides, Christopher (2000). Equilibrium Unemployment Theory (2nd ed.). MIT Press....
7 KB (946 words) - 13:24, 13 July 2024
Hungarian algorithm (category Matching (graph theory))
ISSN 0030-364X. Kőnig's theorem (graph theory) Konig's theorem Vertex cover minimum vertex cover Matching (graph theory) matching Bruff, Derek, The Assignment...
40 KB (5,515 words) - 14:30, 25 August 2024
Berge's theorem (category Matching (graph theory))
In graph theory, Berge's theorem states that a matching M in a graph G is maximum (contains the largest possible number of edges) if and only if there...
6 KB (832 words) - 02:55, 14 May 2023
The theory of random graphs lies at the intersection between graph theory and probability theory. From a mathematical perspective, random graphs are used...
15 KB (2,187 words) - 14:01, 9 January 2024
In the mathematical field of graph theory, a complete bipartite graph or biclique is a special kind of bipartite graph where every vertex of the first...
12 KB (959 words) - 07:51, 18 July 2024
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...
19 KB (2,606 words) - 00:07, 30 April 2024
topological graph theory is a branch of graph theory. It studies the embedding of graphs in surfaces, spatial embeddings of graphs, and graphs as topological...
5 KB (565 words) - 01:25, 16 August 2024
Pfaffian orientation (category Matching (graph theory))
In graph theory, a Pfaffian orientation of an undirected graph assigns a direction to each edge, so that certain cycles (the "even central cycles") have...
6 KB (764 words) - 00:19, 30 April 2024
specifically, it is equivalent to finding a minimum weight matching in a bipartite graph. The following simple example illustrates the importance of...
28 KB (4,534 words) - 03:49, 13 July 2024
up matching in Wiktionary, the free dictionary. Matching may refer to: Matching, Essex, England Matching Green Matching Tye Matching (graph theory), in...
2 KB (264 words) - 19:51, 24 May 2024
Hopcroft–Karp algorithm (category Matching (graph theory))
algorithm) is an algorithm that takes a bipartite graph as input and produces a maximum-cardinality matching as output — a set of as many edges as possible...
25 KB (3,746 words) - 00:21, 30 April 2024
In graph theory, an area of mathematics, a claw-free graph is a graph that does not have a claw as an induced subgraph. A claw is another name for the...
29 KB (3,622 words) - 22:20, 27 May 2024
Telephone number (mathematics) (category Matching (graph theory))
telephone calls. These numbers also describe the number of matchings (the Hosoya index) of a complete graph on n vertices, the number of permutations on n elements...
17 KB (2,039 words) - 15:09, 3 March 2024
Maximally matchable edge (category Matching (graph theory))
In graph theory, a maximally matchable edge in a graph is an edge that is included in at least one maximum-cardinality matching in the graph. An alternative...
7 KB (1,268 words) - 23:23, 22 April 2023