Game colouring of the square of graphs

Abstract

This paper studies the game chromatic number and game colouring number of the square of graphs. In particular, we prove that if G is a forest of maximum degree ∆ ≥ 9, then χg(G ) ≤ colg(G ) ≤ ∆+3, and there are forestsG with colg(G ) = ∆+3. It is also proved that for an outerplanar graph G of maximum degree ∆, χg(G ) ≤ colg(G ) ≤ 2∆ + 14, and for a planar graph G of maximum degree ∆, χg(G ) ≤ colg(G ) ≤ 23∆+ 75.

DOI: 10.1016/j.disc.2009.02.014

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Cite this paper

@article{Esperet2009GameCO, title={Game colouring of the square of graphs}, author={Louis Esperet and Xuding Zhu}, journal={Discrete Mathematics}, year={2009}, volume={309}, pages={4514-4521} }