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