5连通图的分裂和可收缩边

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.

Splitting and Contractible Edges in 5-connected Graphs

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 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.