图的邻域并及度条件与Z_3-连通性  

Neighborhood unions and degree condition and Z_3-connectivity in graphs

作　　者：顾粉霞 蒋梓炜 卢春霞[1] 梁栋[1] 朱佳[1] 杨帆[1] 

机构地区：[1]江苏科技大学数理学院,江苏镇江212003

出　　处：《江苏科技大学学报（自然科学版）》2014年第6期609-612,共4页Journal of Jiangsu University of Science and Technology:Natural Science Edition

基　　金：国家自然科学基金资助项目(11326215);江苏科技大学博士启动项目;2014年本科生创新计划项目

摘　　要：令G是一个2-边连通简单图,且阶数n≥11,令A是一个单位元为0的阿贝尔群.重复收缩图G的非平凡A-连通子图,直到没有这样的子图,所得的新图记为G*,则称G可以A-收缩到G*.文中证明了如果图G满足δ(G)n≤「n/3」-1且对uvE(G),有|N(v)∪N(u)2n|≥「2n/3」-1,那么G不是Z33-连通图当且仅当G可Z3-收缩到{C3,K4,K-4,L}中的一个,其中L是在K4上加一个新点,并且此新点与K4连两条边所得到的简单图.Let G be a 2- edge connected simple graph with n≥11,and A be an abelian group with identity 0.We say that G can be A-reduced to G＊,if G＊is obtained by repeatedly contracting nontrivial A-connected subngraphs until no such a subgraph is left. In this paper,we prove that if δ（G）n≤「n/3」-1 and for uvE（G）,｜N（v）∪N（u）2n｜≥「2n/3」-1,then G is not Zd if and only if G can be Z33-connecte 3-reduced to one of { C3,K4,K-4,L},where L is obtained from K4 by adding a new vertex which is joined to two vertices of K4.

关 键 词：邻域并条件 Z3-连通性 处处非零3-流 

分 类 号：O157.5[理学—数学]