The game colouring number of powers of forests

Stephan Dominique Andres, Winfried Hochstättler

We prove that the game colouring number of the $m$-th power of a forest of maximum degree $\Delta \ge 3$ is bounded from above by \[\frac{(Δ-1)^m-1}{Δ-2}+2^m+1,\] which improves the best…