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In some literature, the term complete matching is used. In the above figure, only part (b) shows a perfect matching. A perfect matching is also a minimum-size edge cover. Thus, the size of a maximum matching is no larger than the size of a minimum edge cover: () . A graph can only contain a perfect matching when the graph has an even ...
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 ...
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 ...
For instance, if G = K m,n, the complete bipartite graph, then the second type of matching polynomial is related to the generalized Laguerre polynomial L n α (x) by the identity: , =! (). If G is the complete graph K n, then M G (x) is an Hermite polynomial:
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 matching in G is a subset M of edge set E , such that every vertex in the vertex set V is adjacent to exactly one edge in M .
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 ...
A matching M is called perfect if every vertex v in V is contained in exactly one hyperedge of M. This is the natural extension of the notion of perfect matching in a graph. A fractional matching M is called perfect if for every vertex v in V, the sum of fractions of hyperedges in M containing v is exactly 1.
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. As each edge will cover exactly two vertices, this ...