A polyhedral approach to edge coloring
Operations Research Letters
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A fundamental theorem of Vizing relates the maximum degree, @D(G), of a simple graph G to the minimum number, "@g(G), of colors needed to color its edges. Vizing's theorem asserts that "@g(G) is either @D(G) or @D(G)+1; however, determining which of these two alternatives holds is NP-complete. We present a polyhedral formulation for determining "@g(G), which we analytically and computationally compare to an earlier set-partitioning formulation. We also establish some valid inequalities for our formulation.