Note On The Game Colouring Number Of Powers Of Graphs

Abstract

We generalize the methods of Esperet and Zhu [6] providing an upper bound for the game colouring number of squares of graphs to obtain upper bounds for the game colouring number of m-th powers of graphs, m ≥ 3, which rely on the maximum degree and the game colouring number of the underlying graph. Furthermore, we improve these bounds in case the underlying graph is a forest.

Keywords

• game colouring number
• marking game
• graph power
• game chromatic number
• forest
• 05c15
• 91a43
• 05c05