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

Authors:
FréDéRic Maffray;Ana Silva
Affiliations:
CNRS, Laboratoire G-SCOP, Grenoble, France;Laboratoire G-SCOP, Université Joseph Fourier, Grenoble, France
Venue:
Discrete Applied Mathematics
Year:
2013

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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.