两圈卡氏积的单射染色  

Injective Coloring of the Cartesian Product of Two Cycles

作　　者：张悦[1] 张莉[1] ZHANG Yue;ZHANG Li(School of Mathematical Sciences,Tongji University,Shanghai,200092,P.R.China)

机构地区：[1]同济大学数学科学学院,上海200092

出　　处：《数学进展》2021年第5期759-771,共13页Advances in Mathematics（China）

基　　金：Supported by NSFC(No.11871377)。

摘　　要：图的单射染色是指图的一种点染色,它要求有公共邻点的两个顶点需染不同颜色.图G的单射色数χi(G)就是指满足图G有一个单射的k-染色的最小的正整数k.本文讨论了两个圈的卡氏积的单射色数问题,并给出了χi(Tm,n)的一些紧的上界以及一些确切值,这里Tm,n=Cm□Cn,m≥3且n≥3.An injective coloring of a graph is a vertex coloring such that any two different vertices with a common neighbor vertex receive distinct colors.The injective chromatic numberχi(G)is the least k such that the graph G has an injective k-coloring.In this paper,we investigate the injective chromatic number of the Cartesian product of two cycles and give some sharp bounds(or exact value)ofχi(Tm,n),where Tm,n=Cm□Cn,m≥3 and n≥3.

关 键 词：单射染色 卡氏积 圈 

分 类 号：O157.5[理学—数学]