2-连通P3-支配图的Hamilton圈

doi:10.3976/j.issn.1002-4026.2011.06.003

山东科学 ›› 2011, Vol. 24 ›› Issue (6): 8-11.doi: 10.3976/j.issn.1002-4026.2011.06.003

2-连通P₃-支配图的Hamilton圈

陈维娜, 王江鲁

山东师范大学数学科学学院，山东济南 250014

收稿日期:2011-05-17 出版日期:2011-12-20 发布日期:2011-12-20

Hamilton cycle of 2-connected P₃-dominated graphs

CHEN Wei-Na, WANG Jiang-Lu

School of Mathematics, Shandong Normal University, Jinan 250014, China

Received:2011-05-17 Online:2011-12-20 Published:2011-12-20

摘要/Abstract

摘要：

如果图G中任意一对距离为2的顶点x,y,有J(x,y)∪J′(x,y)≠Φ,则称G为P₃-支配图。本文证明了：设G是n(≥3)阶2-连通P₃-支配图，如果对G中任意一对不相邻的顶点x,y,有2|N(x)∪N(y)|+d(x)+d(y)≥2n-5,则G含有Hamilton圈或者G∈{K_2,3,K_1,1,3}。

关键词: 半无爪图, P₃-支配图, Hamilton圈

Abstract:

A graph G is a P₃-dominated graph if J(x,y)∪J′(x,y)≠Φ for any pair of vertices x and y of d(x,y)=2.This paper proves that for any pair of nonadjacent vertices x and y in G,which is a 2-connected P₃-dominated graph of order n no less than 3, if 2|N(x)∪N(y)|+d(x)+d(y)≥2n-5, then G has a Hamilton cycle or G∈{K_2,3,K_1,1,3}.

Key words: quasi-claw-free graphs, P₃-dominated graphs, Hamilton cycle

中图分类号:

O157.5

陈维娜, 王江鲁. 2-连通P₃-支配图的Hamilton圈[J]. 山东科学, 2011, 24(6): 8-11.

CHEN Wei-Na, WANG Jiang-Lu. Hamilton cycle of 2-connected P₃-dominated graphs[J]. Shandong Science, 2011, 24(6): 8-11.

2-连通P₃-支配图的Hamilton圈

Hamilton cycle of 2-connected P₃-dominated graphs

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