Question

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Let d(x) and d(y) stand for the degrees of vertices x and y in G, respectively. Let G[X,Y] be a bipartite graph, each vertex of which is joined to at least one, but not all, vertices in the other part. Suppose that d(2) > d(y) for all xy € E. Show that |Y| > |X|, with equality if and only if d(x) = d(y) for all xy € E with x € X and Y EY.

Answer 1

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