Note on the game colouring number of powers of graphs
Stephan Dominique Andres, Andrea Theuser · Discussiones Mathematicae Graph Theory · 2015
We generalize the methods of Esperet and Zhu [6] providing an upper bound for the game colouring number of squares of graphs to obtain upper bounds for the game colouring number of m-th powers of graphs, m 3, which rely on the maximum degree and the game colouring number of the underlying graph. Furthermore, we improve these bounds in case the underlying graph is a forest.