邻集交、邻集并与图的哈密尔顿性  

Neighborhood Intersections and Unions & Hamiltonian Properties in Graphs

作　　者：刘亚春[1] 

机构地区：[1]中南工学院基础课部

出　　处：《中南工学院学报》1995年第1期13-16,共4页

摘　　要：本文把不相邻两点的邻集交与邻集并两个概念揉合在一起，以之刻划了比较广泛的一类哈密尔顿图、可迹图及哈密尔顿连通图．文中证明了：若ｓ，ｔ是两个整常数，ｔ≥２，图Ｇ是阶为Ｐ的２连通图，对任何不相邻的顶点ｘ与ｙ，若它们邻集交以ｓ为下界，邻集并以（ｔｐ—ｓ）／（ｔ＋１）为下界，则Ｇ是哈密尔顿图．当把连通度和邻集并的下界稍微减少或增大时，图Ｇ减弱为可迹图或加强为哈密尔顿连通图．This paper has some new sufficient conditions with neighborhood intersections and unions about hamiltonian properties in graphs. It is proved that if s,t are integeral constants, where t≥2, G is 2-connected graph with order p, and for any pair of venices x and y, xy E (G), |N (x) ∪N (y) |≥(tp-s) / (t+1), |N (x) ∩N (y) |≥s. Then G is hamiltonian,by decreasing or increasing the sufficient condition,the result abovt traceable or hamiltonian connected graphs be also presented.

关 键 词：可迹图 连通图 哈密顿图 领集交 邻集并 

分 类 号：O144[理学—数学] O157.5[理学—基础数学]