When.com Web Search

Search results

  1. Results From The WOW.Com Content Network
  2. Matching (graph theory) - Wikipedia

    en.wikipedia.org/wiki/Matching_(graph_theory)

    A maximal matching is a matching M of a graph G that is not a subset of any other matching. A matching M of a graph G is maximal if every edge in G has a non-empty intersection with at least one edge in M. The following figure shows examples of maximal matchings (red) in three graphs. A maximum matching (also known as maximum-cardinality ...

  3. Perfect matching - Wikipedia

    en.wikipedia.org/wiki/Perfect_matching

    A perfect matching can only occur when the graph has an even number of vertices. A near-perfect matching is one in which exactly one vertex is unmatched. This can only occur when the graph has an odd number of vertices, and such a matching must be maximum. In the above figure, part (c) shows a near-perfect matching.

  4. Maximum cardinality matching - Wikipedia

    en.wikipedia.org/wiki/Maximum_cardinality_matching

    Maximum cardinality matching is a fundamental problem in graph theory. [1] We are given a graph G , and the goal is to find a matching containing as many edges as possible; that is, a maximum cardinality subset of the edges such that each vertex is adjacent to at most one edge of the subset.

  5. Petersen's theorem - Wikipedia

    en.wikipedia.org/wiki/Petersen's_theorem

    In a cubic graph with a perfect matching, the edges that are not in the perfect matching form a 2-factor. By orienting the 2-factor, the edges of the perfect matching can be extended to paths of length three, say by taking the outward-oriented edges. This shows that every cubic, bridgeless graph decomposes into edge-disjoint paths of length ...

  6. Graph matching - Wikipedia

    en.wikipedia.org/wiki/Graph_matching

    The case of exact graph matching is known as the graph isomorphism problem. [1] The problem of exact matching of a graph to a part of another graph is called subgraph isomorphism problem. Inexact graph matching refers to matching problems when exact matching is impossible, e.g., when the number of vertices in the two graphs are different. In ...

  7. Matching polynomial - Wikipedia

    en.wikipedia.org/wiki/Matching_polynomial

    The Hosoya index of a graph G, its number of matchings, is used in chemoinformatics as a structural descriptor of a molecular graph. It may be evaluated as m G (1) (Gutman 1991). The third type of matching polynomial was introduced by Farrell (1980) as a version of the "acyclic polynomial" used in chemistry.

  8. Maximum weight matching - Wikipedia

    en.wikipedia.org/wiki/Maximum_weight_matching

    In 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 is maximized. A special case of it is the assignment problem , in which the input is restricted to be a bipartite graph , and the matching constrained to be have cardinality that of the ...

  9. Factor-critical graph - Wikipedia

    en.wikipedia.org/wiki/Factor-critical_graph

    In graph theory, a mathematical discipline, a factor-critical graph (or hypomatchable graph [1] [2]) is a graph with n vertices in which every induced subgraph of n − 1 vertices has a perfect matching. (A perfect matching in a graph is a subset of its edges with the property that each of its vertices is the endpoint of exactly one of the ...