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 graph multicoloring, where each vertex requires a multiplicity of colors, graph bandwidth coloring, where the colors assigned to adjacent vertices must differ by at least a given distance, and graph bandwidth multicoloring, which generalizes both the multicoloring and the bandwidth coloring problems. We report some computational evidence of the effectiveness of the new branching scheme.
branching scheme graph bandwidth multicoloring graph coloring