Halin图的消圈数及点染色问题  

The decycling number and vertex coloring of Halin graphs

作　　者：王永强[1] 任韩[1] 

机构地区：[1]华东师范大学数学系,上海200241

出　　处：《华东师范大学学报（自然科学版）》2016年第6期65-70,共6页Journal of East China Normal University(Natural Science)

基　　金：国家自然科学基金(11171114);上海市自然科学基金(13dz2260400)

摘　　要：Tutte关于3-连通图的结构定理表明:每一个3-连通图都可由某个轮图(也是Halin图)经顶点分裂逐步得到.这表明了Halin图在图结构研究中的地位和作用.首先研究得到了近正则Halin图的消圈数的上、下界并证明了上述界是紧的,接着得到了最大度为k或最小度为k的Halin图的消圈数所满足的界;此外还研究了Halin图的点染色问题,给出了它的点色数定理的一个新证明.According to the structural theorem of 3-connected graphs by Tutte, every 3-connected graph can be obtained by splitting vertices of some wheel which is Halin graph, which indicates that the study of the structure of Halin graph is important in graph structures. In this paper, firstly we dealt with the decycling number of the nearly k-regular Halin graphs, and we got the bidirectional inequality that the decycling numbers of nearly regular Halin graphs must satisfy, then we proved that the boundaries above are tight and got the boundaries of Halin graphs with the most biggest degree or the least degree k. At last, we gave a new proof to the theorem about the （vertex） coloring of Halin graphs.

关 键 词：近正则Halin图 最小消圈集 消圈数 点色数 

分 类 号：O157.5[理学—数学]