A simple branching scheme for vertex coloring problems

We present a branching scheme for some Vertex Coloring Problems based on a new graph operator called extension. The extension operator is used to generalize the branching scheme proposed by Zykov for the basic problem to a broad class of coloring problems, such as the graph multicoloring, where each vertex requires a multiplicity of colors, the graph bandwidth coloring, where the colors assigned to adjacent vertices must differ by at least a given distance, and graph bandwidth multicoloring, that generalizes both the multicoloring and the bandwidth coloring problems. We report some computational evidence of the new branching scheme effectiveness.