【摘要】 关于哈密尔顿连通图的一个基本结果是Ore给出的：设G是n阶图,若对于任意两个不相邻顶点u和v,有d（u）+d（v）≥n+1,则G是哈密尔顿连通的．设G是一个图,对于任意u （?）V（G）,令N（U）=∪_u∈∪N（u）,d（U）=|N（U）|,称d（U）是U的度．本文利用独立集的度和得到如下结果：设s和t是正整数,G是（2s+2t+1）-连通n阶图．若对于任两个强不交独立集S,T,|S|=s,|T|=t,有d（S）+d（T）≥n+1．则G是哈密尔顿连通的．同时也得到图的哈密尔顿性的其它相关结果．两个独立集S和T称为强不交的,如果S∪T也是独立集．更多还原

【Abstract】 One of the fundamental results concerning hamiltonian-connected graphs is due to Ore:If G is a graph of order n≥3 such that d（u）+d（v）≥n+1 for every pair of nonadjacent vertices u,v∈V（G）,then G is hamiltonian-connected.Let G be a graph, for any V（?）V（G）,let N（U）=U_u∈UN（u）,d（U）=|N（U）|.In this paper,we give the following result:Let s and t be two positive integers and G be a（2s+2t+1）-connected graph of order n.If d（S）+d（T）≥n+1 for every two strongly disjoint independent sets S and T with |S|=s and |T|=t,then G is hamiltonian-connected.Other related results are obtained too.更多还原