设Ｇ是一个图，Ｂ ＝ ｛ｖ ∈Ｖ（Ｇ）｜〈Ｎ（ｖ）〉不连通｝．如果Ｂ是独立集，并且ｖ ∈Ｂ，ｕ ∈Ｖ（Ｇ）， 使〈Ｎ（ｕ） ∪｛ｕ｝〉连通，则称Ｇ是几乎局部连通图．本文证明：连通、几乎局部连通无爪图是完全圈可扩的．

A graph $G$ is almost locally connected if $B={v∈V(G)|〈N(v)〉$is not connected} is an independent set and, for every $v∈B,u∈V(G)$ such that $〈N(u)∪{u}〉is connected. In this paper, it is proved that every connected, almost locally connected $K\-\{1,3\}$\|free graph is fully cycle extendable.