连通、几乎局部连通拟无爪图是完全圈可扩的  

EVERY CONNECTED, ALMOST LOCALLY CONNECTED QUASI-CLAW-FREE GRAPH IS FULLY CYCLE EXTENDABLE

作　　者：滕延燕[1] 尤海燕[1] 王江鲁(指导) 

机构地区：[1]山东师范大学数学系,济南250014 [2]不详

出　　处：《山东师范大学学报（自然科学版）》2002年第4期5-8,共4页Journal of Shandong Normal University(Natural Science)

基　　金：山东省教委科技计划项目 (J 0 1P 0 1)

摘　　要：G是一个图 ,B(G)表示G中所有局部不连通的点构成的集合 .如果B(G)是独立集 ,并且对任意v∈B(G) , u∈V(G) ,使G[N(v)∪ {u}]连通 ,则称G是几乎局部连通的 .如果G中所有爪心构成的集合D(G)是独立集 ,并且对任意v∈D(G) ,G[N(v) ]是强 2 -控制的 ,则称G是拟无爪图 .本文证明 :连通、几乎局部连通的拟无爪图是完全圈可扩的 .A graph G is called almost locally connected if B(G)={v∈V(G):Gis not connected} is independent and for any v ∈B(G),there exists u in V(G) such that G is connected.We say that G is a quasi-claw-free graph if the set of claw centers of G is independent and Gis strong 2-dominated for any claw center v of G.It is shown that every connected,almost locally connected quasi-claw-free graph of order at least 3 is fully cycle extendable.

关 键 词：几乎局部连通图 拟无爪图 完全圈可扩图 独立集 连通图 强控制集 

分 类 号：O157.5[理学—数学]