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.

Source : oai:arXiv.org:1505.05718

Volume: Vol. 18 no. 1

Section: Graph Theory

Published on: November 24, 2015

Submitted on: November 24, 2015

Keywords: Mathematics - Combinatorics,05C15, 91A43, 05C05

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