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

نویسندگان

Jiaojiao Wu

Xuding Zhu

چکیده

This paper discusses the game colouring number of partial k-trees and planar graphs. Let colg(PT k) and colg(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 colg(PT k) = 3k + 2 and colg(P) ≥ 11. We also prove that the game colouring number colg(G) of a graph is a monotone parameter, i.e., if H is a subgraph of G, then colg(H) ≤ colg(G).

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