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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 ...
In graph theory, a perfect matching in a graph is a matching that covers every vertex of the graph. ... In some literature, the term complete matching is used.
a finite graph is planar if and only if it contains no subgraph homeomorphic to K 5 (complete graph on five vertices) or K 3,3 (complete bipartite graph on two partitions of size three). Vijay Vazirani generalized the FKT algorithm to graphs that do not contain a subgraph homeomorphic to K 3,3. [11]
In graph theory, the matching polytope of a given graph is a geometric object representing the possible matchings in the graph. ... and the complete graph on 4 vertices.
An example of a bipartite graph, with a maximum matching (blue) and minimum vertex cover (red) both of size six. In the mathematical area of graph theory, Kőnig's theorem, proved by Dénes Kőnig (), describes an equivalence between the maximum matching problem and the minimum vertex cover problem in bipartite graphs.
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 ...
A vertex is matched or saturated if it is one of the endpoints of an edge in the matching. A perfect matching or complete matching is a matching that matches every vertex; it may also be called a 1-factor, and can only exist when the order is even. A near-perfect matching, in a graph with odd order, is one that saturates all but one vertex.
An graph (or a component) with an odd number of vertices cannot have a perfect matching, since there will always be a vertex left alone. The goal is to characterize all graphs that do not have a perfect matching. Start with the most obvious case of a graph without a perfect matching: a graph with an odd number of vertices.