The game colouring number of powers of forests

Stephan Dominique Andres, Winfried Hochstättler

Published 2015-05-21Version 1

We prove that the game colouring number of the $m$-th power of a forest of maximum degree $\Delta\ge3$ is bounded from above by \[\frac{(\Delta-1)^m-1}{\Delta-1}+2^m+1,\] which improves the best known bound by an asymptotic factor of 2.