图是极大3限制边联通的充分条件

设S是连通图G中的一个边子集。若G S不连通且它的每个连通分支的阶至少为k，则称S是G的一个k限制边割。图G的最小k限制边割的边数称为G的k限制边连通度，记为λκ(G)。定义ξκ(G)=min{|［X,X］|:|X|=k,G［X］连通}，其中X=V(G)＼X。若λk (G)=ξk(G)，则称G是极大k限制边连通的。设G是一个围长至少为5的λ3 连通图。本文证明了若G中不存在5个点u1，u2，v1，v2，v3使得d(ui,vj)≥3(i=1,2;j=1,2,3)，则G是极大3限制边连通的。

Sufficient conditions of a maximally 3-restricted edge connected graph

Let S be an edge subset in a connected graph G. S is a k restricted edge cut if G S is disconnected and the order of its every connected branch is at least k.The cardinality of a minimum k restricted edge cut of graph G is denoted by λκ (G).Let ξκ(G)=min{|［X,X］|:|X|=k,G［X］is connected}, where X=V(G)＼X. A graph G is maximally k restricted edge connected if λk(G)=ξk(G). Let G be a λ3 connected graph with girth more than five. We prove that G is maximally 3 restricted edge connected if it does not contain five vertices u1,u2,v1,v2,v3 satisfying d(ui,vj)≥3(i=1,2;j=1,2,3).