摘要
Mycielski图是在1955年由Mycielski首先提出的,推广的Mycielski图是在2003年由Peter Che Bor Lam,林文松等给出的Mycielski图的一个自然推广,且研究了它的圆色数.目前关于推广的Mycielski图性质以及它们在点色数,分数色数,圆色数等方面已有许多研究.本文定义了推广的Mycielski图的另一推广称为类推广的Mycielski图,且探讨了推广的Mycielski图和类推广的Mycielski图在全染色、邻点可区别全染色方面与原基础图的关系,从而也得到了它们满足全染色猜想和邻点可区别全染色猜想及它们达到全色数和邻点可区别的全色数的下界的一些充分条件.
Mycielski＇s graph was first introduced by Mycielski in 1955, generalized Mycielski＇s graph was introduced the natural generalization of Mycielski＇s graph by Peter Cher Dor Lam, Lin Wensong etc. in 2003, and studied circular chromatic number of it. At present, there were some results of basic properties of generalized Mycielski＇s graph and vertex chromatic number, fractional chromatic number, circular chromatic number and so on. In this paper, we define similar generalized Mycielski＇s graph which is another generalization of generalized Mycielski＇s graph, and we deal with the relations between the basic graphs and their generalized Mycielski＇s graph or similar generalized Mycielski＇s graph on the total coloring and the adjacent vertex-distinguish total coloring. And we obtain some sufficient conditions with which the constructional graphs satisfy the total coloring conjectrue and adjacent vertex-distinguish total coloring conjectrue, and with which they reach lower bound of the total chromatic number and the adjacent vertex-distinguishing total chromatic number.
出处
《数学进展》
CSCD
北大核心
2010年第1期88-94,共7页
Advances in Mathematics（China）
基金
国家自然科学基金(No.60673047).
