5连通图的分裂和可收缩边-《集美大学学报（自然科学版）》

文章信息/Info

Author(s):: XU Li-qiong; (School of Science,Jimei University,Xiamen 361021,China)

摘要:: ］引入5连通图中度为5的顶点的分裂，利用分裂和收缩的运算对某类5连通图进行归纳，证明了对于阶至少为7的5连通图G，当G的任一断片的阶不等于2，且对G的任一5度顶点z,G[NG(z)]中含子图(K2∪2K1)+K1，则对G的任意顶点x，下列断言之一成立：1）x关联一条可收缩边；2）在NG(x)中存在一个5度顶点y关联一条可收缩边；3）在NG(x)中存在一个5度顶点y，使得对y作某一个分裂运算所得的图是5连通的

Abstract:: The splitting operation at a vertex of degree five in a 5-connected graph was defined,and proved that,for a 5-connected graph G with order at least seven,if the order of any end in G was not equal to 2,and for any vertex z of degree five, G[NG(z)]contained a subgraph(K2∪2K1)+K1,then,for any x in V(G),one of the followings held:1)A contractible edge was incident with x;2)There existed a vertex y of degree five in NG(x) such that a contractible edge was incident with y;3)There existed a vertex y of degree five in NG(x) such that after some splitting at y in G,the resulting graph was 5-connected