Coloring powers of graphs of bounded clique-width

Abstract

Given a graph G, the graph Gl has the same vertex set and two vertices are adjacent in Gl if and only if they are at distance at most l in G. The l-coloring problem consists in finding an optimal vertex coloring of the graph Gl, where G the input graph. We show that, for any fixed value of l, the l-coloring problem is polynomial when restricted to graphs of bounded clique-width, if an expression of the graph is also part of the input. © Springer-Verlag Berlin Heidelberg 2003.