用基本集讨论k－连通图的Hamilton－连通性

A Discussion on k-Connected Graphs Being Hamilton-Connected Using Essential Sets

设Ｇ是ｎ阶ｋ－连通图（ｋ≥３）．称Ｇ的独立集Ｓ为一个基本集，如果存在｛ｕ，ｖ｝Ｓ使得ｄｉｓｔ（ｕ，ｖ）＝２．本文证明了下述结论：如果对Ｇ的任－ｋ－基本集Ｓ，有ｍａｘ｛ｄ（ｕ）｜ｕＳ｝≥ 则Ｇ或者是Ｈａｍｉｌｔｏｎ－连通的或者属于两类例外图之一。

Let G be a k-connected(k≥3) graph of order n. An independent set S of G is called essential if there exists ,such that dist(u,v)=2. In this paper we shall prove that if for any essential set S with k venices of G,then either G is Hamilton-connected or G is one of two classes of exceptional graphs.