B-colouring the Cartesian product of trees and some other graphs

Abstract

A b-colouring of a graph is a colouring of its vertices such that every colour class contains a vertex that has a neighbour in all other classes. The b-chromatic number of a graph is the largest integer k such that the graph has a b-colouring with k colours. We show how to find in polynomial time an optimal b-colouring of the Cartesian product of trees by paths, cycles and stars. © 2011 Elsevier B.V. All rights reserved.