Game Chromatic Number of Graphs
暂无分享，去创建一个
y Abstract We show that if a graph has acyclic chromatic number k, then its game chromatic number is at most k(k + 1). By applying the known upper bounds for the acyclic chromatic numbers of various classes of graphs, we obtain upper bounds for the game chromatic number of these classes of graphs. In particular, since a planar graph has acyclic chromatic number at most 5, we conclude that the game chromatic number of a planar graph is at most 30, which improves the previous known upper bound for the game chromatic number of planar graphs.
[1] M. Albertson,et al. An acyclic analogue to Heawood's theorem , 1978 .
[2] Hal A. Kierstead,et al. Planar Graph Coloring with an Uncooperative Partner , 1994, Planar Graphs.
[3] Wayne Goddard,et al. Acyclic colorings of planar graphs , 1991, Discret. Math..
[4] U. Faigle,et al. On the game chromatic number of some classes of graphs , 1991 .
[5] Oleg V. Borodin,et al. On acyclic colorings of planar graphs , 2006, Discret. Math..