围长g>7的极大5限制边连通图的充分条件

A Sufficient Condition for Maximally 5-Restricted Edge Connected Graphs with Girth g>7

设G=(V,E)是一个λk-连通图,称图G的λk-割所含边的数目为G的k限制边连通度.定义ξk(G)=min{|[X,Y]|∶|X|=k,G[X]连通,Y=V(G)\X}.拟研究λ5(G)=ξ5(G)的围长条件.

For aλk-connected G=(V,E),the k-restricted edge connectivity of G,denoted byλk(G),was defined as the cardinality of a minimumλk-cut.Letξk(G)=min{|[X,Y]|∶|X|=k,G[X]is connected,where Y=V(G)\X}.In this paper,a girth condition was presented for graphs to be maximally 5-restricted edge connected.