3-正则3-连通图的圈上的可去边分布  

Distribution of Removable Edges in the Cycles of 3-Regular 3-Connected Graphs

作　　者：覃城阜 杨海玲 梁宇 QIN Cheng-fu;YANG Hai-ling;LIANG Yu(School of Mathematics and Statistics,Nanning Normal University,Nanning 530100,China;College of General Education,Nanning University,Nanning 530299,China;Center for Applied Mathematics of Guangxi,Nanning Normal University,Nanning 530100,China)

机构地区：[1]南宁师范大学数学与统计学院,广西南宁530100 [2]南宁学院通识教育学院,广西南宁530299 [3]南宁师范大学广西应用数学中心,广西南宁530100

出　　处：《南宁师范大学学报（自然科学版）》2023年第2期7-10,共4页Journal of Nanning Normal University：Natural Science Edition

基　　金：国家自然科学基金(11961051)。

摘　　要：设G是k-连通图,e是G的一条边,由G-e经过删除度为k-1的顶点u,并用完全图K_(k-1)代替导出子图(G-e)[N(u)]得到的图记为G■e.若G■e仍是k-连通的,则称e是可去边.该文证明了3-正则3-连通图的最长圈至少有4条可去边,且有无穷多的例子说明这个界可达到.Let G be a k-connected graph and e an edge of G.Denote by G■e the graph obtained from G-e by deleting each vertex u of degree k-1 in G-e and replacing the induced subgraph(G-e)[N(u)]with the complete graph K_(k-1).An edge e is said to be removable if G■e is also k-connected.We show that each longest cycle of a 3-connected cubic graph has at least four removable edges,and there are infinitely many graphs that attain this bound.

关 键 词：3-正则3-连通图 可去边 圈 

分 类 号：O157.5[理学—数学]