The game colouring number of powers of forests

Abstract

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 \[\frac{(\Delta-1)^m-1}{\Delta-2}+2^m+1,\] which improves the best known bound by an asymptotic factor of 2.

Keywords

• mathematics - combinatorics
• 05c15, 91a43, 05c05