Lower bounds for the game colouring number of partial k-trees and planar graphs

Abstract: This paper discusses the game colouring number of partial k-trees and planar graphs. Let and denote the maximum game colouring number of partial k trees and the maximum game colouring number of planar graphs, respectively. In this paper, we prove that and . We also prove that the game colouring number of a graph is a monotone parameter, i.e., if is a subgraph of , then . [Copyright &y& Elsevier]