y interested in the maximum matching problem; that is, th problem of nding a matching of maximum cardinality. For simplicity, we refer to a matching of maximum cardinality as a maximum matching, and let (G) denote the size of a maximum matching in G. Let M be a matching in G, and let v be a vertex of G. If v is the end of an edge in M , then we say that M saturates v. The set of all vertices saturated by a particular matching is called a matchable set of G. Note that, since each edge saturates two vertices, matchable sets have even cardinality. A matching that saturates every vertex is called perfect. The perfect matching problem is the problem of deciding whether a graph has a perfect matching. Obviously, G

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