Question: Let G be a connected bipartite graph with bipartition (A, B) such that |A| = |B|. Suppose that for every edge e E(G), there is

Let G be a connected bipartite graph with bipartition (A, B) such that |A| = |B|. Suppose that for every edge e E(G), there is a perfect matching containing e. Prove that for every proper nonempty subset D of A, |N(D)| > |D|.

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