圈关联对策染色的研究

Research on the Incidence Game Chromatic Number of Cycles

Stephan提出了图关联对策染色的概念:设G是一个有限图,两个人Alice和Bob轮流对图G的关联进行染色,使得相邻的关联染色不同,Alice首先开始染色,若无法再进行下去时染色结束.若染色结束后图G的每个关联都正常染色,则Alice获胜,否则Bob获胜.本文讨论了圈关联对策染色,并确定了圈关联对策色数.

The definition of incidence game chromatic number of graph was proposed by Stephan. Let G be a finite graph. Two players, Alice and Bob, color alternately the incidences of graph in such a way that the neighborly incidences receive distinct colors. The game ends when this is not possible any more. Alice wins if every incidence is colored at the end of the game, otherwise Bob wins. In this paper, we discuss the indidence game coloring of cycle, and determine the incidence game chromatic number of cycle.