Matching structure graph edges from "summary" of Introduction to Graph Theory by Douglas Brent West
A matching in a graph G is a set of pairwise nonadjacent edges. That is, no two edges in a matching share a common endpoint. The simplest example of a matching is the empty set, which contains no edges. A matching of size 1 consists of a single edge, a matching of size 2 is a pair of nonadjacent edges, and so on. In general, a matching in a graph G is a set of edges no two of which are adjacent. A matching of maximum size is called a maximum matching. If G has a matching of size k, where k is the largest possible, then G has a maximum matching. The size of a maximum matching is denoted by α'(G). The matching k in a graph G is a maximum matching if no other matching in G has more edges than k. A matching of maximum size that saturates every vertex in G is called a perfect matching. If G has a perfect matching, then G is said to be a factor-critical graph. ...
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