一类图的点圈扩张性

Extendable Cycles in a Graph

本文的主要结果是：设G是2-连通图．若，则G的每个点v都在3-圈或4-圈或5-圈上，并可由此出发经过若干次1或2-扩张，最后得到Hamilton圈．

The following result is proved:Let G be a 2-connected,if the independence number of vertices at a distance 2 from a vetexin G is one. Then each vertex v∈V(G) is on a 3-cycle or on a 4-cycle or on a 5-cycle,which canbe extended to a Hamilton cycle through a series of 1 or 2-extensions.