K_(1,p)-约束图的完全圈可扩性

FULLY CYCLE EXTENDABILITY OF K 1,p CONTROLLED GRAPHS

本文定义了一个新的图类——Ｋ１，ｐ－约束图，它包含了无爪图和几乎无爪图．本文证明：顶点数不小于３的连通、局部连通的Ｋ１，ｐ－约束图是完全圈可扩的．这一结果包含了Ｈｅｎｄｒｙ和Ｒｙｊａｃ∨ｅｋ在无爪图和几乎无爪图上的相应结果．

In this paper,a new class of graphs is defined which contains claw free graphs and almost claw free graphs.It is called K 1,p controlled graph.The authors prove that every connected,locally connected K 1,p controlled graph on at least three vertices is fully cycle extendable.This result includes the corresponding results on claw free graphs and almost claw free graphs obtained by Hendry and Ryjác ∨ek.