h-连通图中可收缩边的存在定理

The existence theorem of contractible edges in h-connected graphs

设 G是 h-连通的简单非完全图 ,对 G中的任一条边 uv,用 du,dv表示顶点 u、v的度 ,若 du + dv≥ 5 h/ 2 -1,则图 G存在可收缩边 ,从而推广了 Yoshimi Egam a[1 ]的结论 .

Let G be a h connected simple non complete graph, in this paper, it is proved that if du+dv ≥5h/2-1 for any edge uv of G, then G has at least one h contractible edge