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Edge coloring the edge chromatic number Xe (G) of a graph G is the minimum number of colors needed for coloring the edges of G so that incident edges get different colors. Clearly, Xe (G) > max d(u), where d(u) is the degree of vertex u. If G = (S, T; E) is bipartite, the equality sign holds. Prove this for Kn,n. Discuss.

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