Study On The Problem About The Chromatic Game Of Graphs

The chromatic theory of graphs is one of the most important branches of Graph Theory. In particular, the study on the game chromatic number of graphs is very noticeable and very useful in design of networks and computer science. So far, many results on the existence of game chromatic number of graphs have been proposed. Recently a lot of problems have been studied, as follows: game chromatic, edge game chromatic, relaxed game chromatic.In this paper, we first study the game chromatic number on graphs, and then we give some examples for the lower bound about the game chromatic number of the planar graphs. We study the split method on the problem of edge game chromatc number of trees. Then we investigate a variation of the edge game chromatic number of a graph called edge game chromatic numberâ…¡, and also we give the upbound of edge game chromatic number II of some simple graphs.The main work of this paper is that we have given the edge game chromatic number of cycle likes, fan graphs, flowers, Halin graphs, and the upbound is sharp for cycle likes and Halin graphs, it is also a good example for the study of planar and outerplanar graphs.At last, we learn the property of the problem on the relaxed game chromatic on graphs. Then we introduce the concept of edge relaxed game chromatic number, and we give the upbound of edge relaxed game chromatic number of chain and cycle.