b-colouring the Cartesian product of trees and some other graphs ?
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 k such that the graph has a b-colouring with k 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.
b-colouring cartesian product tree b-chromatic number exact algorithm