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 col g ( PT k ) and col g ( P ) 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 col g ( PT k ) = 3 k + 2 and col g ( P ) ⩾ 11 . We also prove that the game colouring number col g ( G ) of a graph is a monotone parameter, i.e., if H is a subgraph of G , then col g ( H ) ⩽ col g ( G ) .