极大3限制边连通二部图的充分条件  

A Sufficient Condition for Maximally 3-restricted Edge-connected Bipartite Graphs

作　　者：张磊[1] ZHANG Lei(School of Mathematics,Jinzhong University,Jinzhong 030619,China)

机构地区：[1]晋中学院数学学院,山西晋中030619

出　　处：《数学的实践与认识》2021年第1期302-307,共6页Mathematics in Practice and Theory

基　　金：2016年度晋中学院博士基金科研项目(bsjj2016202);晋中学院创客团队项目(jzxycktd2019023)。

摘　　要：设G=(V,E)是一个连通图.称一个边集合S■E是一个k限制边割,如果G-S的每个连通分支至少有k个顶点.称G的所有k限制边割中所含边数最少的边割的基数为G的k限制边连通度,记为λ_k(G).定义ξ_k(G)=min{[X,■]:|X|=k,G[X]连通,■=V(G)\X}.称图G是极大k限制边连通的,如果λ_k(G)=ξ_k(G).本文给出了围长为g>6的极大3限制边连通二部图的充分条件.For a connected network G=(V,E),an edge set S■E is a k-restricted edge cut if G-S is disconnected and every component of G-S has at least k vertices.The k-restricted edge connectivity of G,denoted byλ_k(G),is defined as the cardinality of a minimum k-restricted edge cut.Letξ_k(G)=min{|[X,Y]|:|X|=k,G[X]is connected},where Y=V\X.A graph G is maximally k-restricted edge connected ifλ_k(G)=ξ_k(G).In this paper,a sufficient condition is presented for bipartite graphs with girth g>6 to be maximally 3-restricted edge connected.

关 键 词：互连网络 二部图 3限制边连通度 点集对 

分 类 号：O157.5[理学—数学]