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.
Maffray, F., & Silva, A. (2013). B-colouring the Cartesian product of trees and some other graphs. In Discrete Applied Mathematics (Vol. 161, pp. 650–669). https://doi.org/10.1016/j.dam.2011.06.019