θ-图的对策着色和对策色数  

The Game Coloring and Chromatic Number of θ-Graph

作　　者：亢琳[1] 杨爱民[1] 

机构地区：[1]山西大学数学科学学院,山西太原030006

出　　处：《中北大学学报（自然科学版）》2009年第1期5-7,共3页Journal of North University of China(Natural Science Edition)

基　　金：国家自然科学基金资助项目(60773131)

摘　　要：介绍了一种新的二人对策着色:色对策Ⅱ和对策色数Ⅱ.比较了两种色对策的差异,讨论了图G的色对策Ⅱ的性质.在路图和图圈的基础上,利用顶点标号的方法,分别对θ-图和广义θ-图分情况进行了讨论,并得出了它们的对策色数Ⅱ.给出了二人对策着色中使选手A获胜的策略,并推广了此结论.得出了均匀θ-图的对策色数Ⅱ,给出了二人对策着色中选手A的获胜策略.First, this paper introduces a new two-person game coloring, game chromatic and game chromatic number. Their difference is compared, and the properties of the game chromatic number Ⅱ are discussed. Second, on the basis of the path and cycle, the game chromatic numbers of θ-graph and general θ-graph are obtained respectively, and the winning strategy for A player is presented. Finally, the results are extended to obtain the game chromatic number of even θ-graph, and the winning strategy for A player is given.

关 键 词：对策着色 对策色数Ⅱ Θ-图 广义θ-图 

分 类 号：O157.5[理学—数学]