二部图中最大匹配的存在性 Theorem 8.3 Let G be a bipartite graph with partite sets U and W such that r=Us W.Then G contains a matching of cardinality r if and only if G satisfies Hall's condition. For a nonempty set X of U the neighborhood MX)of X is the union of the neighborhoods Mx).Equivalently,MX)consists of all those vertices of W that are the neighbors of one or more vertices in X.The graph G is said to satisfy Hall's condition if MX) for every nonempty subset Xof U.二部图中最大匹配的存在性 For a nonempty set X of U, the neighborhood N(X) of X is the union of the neighborhoods N(x). Equivalently, N(X) consists of all those vertices of W that are the neighbors of one or more vertices in X. The graph G is said to satisfy Hall’s condition if |N(X)| ≥ |X| for every nonempty subset X of U