A New Activation Strategy Of Relaxed Coloring Game On Partial K-Tree

This paper studies the relaxed game chromatic number of partial k-tree with the relaxed degree d. The concept of the relaxed game chromatic number of a graph was firstly introduced by Chou, Wang and Zhu in [1]. It connects the coloring problem with the game theory, so it is a important subject in the graph coloring theory and is studied by many researchers. About the definition of the relaxed game chromatic number of a graph, we will introduce it in the definition 3.1.3.The relaxed game chromatic number of tree, outerplanar graphs, partial k-tree and pseudo partial k-tree have been studied by many researchers home and abroad, this paper further studied the relaxed game chromatic number of partial k-tree based on the known research, according to appling a new activation strategy, we proved if the relaxed degree d > 2k + 1, then for this (r, d)-relaxed coloring game, we have (2k + 1) - Xg(G) < k + 1, it is an improvement about the result in paper [2].