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  2. Maximum weight matching - Wikipedia

    en.wikipedia.org/wiki/Maximum_weight_matching

    The first is also a perfect matching, while the second is far from it with 4 vertices unaccounted for, but has high value weights compared to the other edges in the graph. 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.

  3. Matching (graph theory) - Wikipedia

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

    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 matching [2]) is a matching that contains the largest possible number of edges. There may be many ...

  4. 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 .

  5. List of NP-complete problems - Wikipedia

    en.wikipedia.org/wiki/List_of_NP-complete_problems

    Minor testing (checking whether an input graph contains an input graph as a minor); the same holds with topological minors; Steiner tree, or Minimum spanning tree for a subset of the vertices of a graph. [2] (The minimum spanning tree for an entire graph is solvable in polynomial time.) Modularity maximization [5]

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  7. Graph matching - Wikipedia

    en.wikipedia.org/wiki/Graph_matching

    Graph matching is the problem of finding a similarity between graphs. [ 1 ] Graphs are commonly used to encode structural information in many fields, including computer vision and pattern recognition , and graph matching is an important tool in these areas. [ 2 ]

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  9. Blossom algorithm - Wikipedia

    en.wikipedia.org/wiki/Blossom_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, [1] and published in 1965. [2] Given a general graph G = (V, E), the algorithm finds a matching M such that each vertex in V is incident with at most one edge in M and | M | is maximized. The ...