Web Reference: 1 Matching Definition 1. A matching in a graph G is a subgraph M of G in which every vertex has degree 1. I.e. a matching is a disjoint set of edges with their endpoints. We often equate a matching M with its edge set. Example: M is a matching of size 2 in G. In the switching context (where all edge weights are nonnegative) any maximum matching or maximum weighted matching is also a maximal matching, but neither converse is generally true. The problem was also studied in a model where clients may switch servers in order to improve the matching, and the goal is to economize on the number of switches while achieving a maximum matching.
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