Sharp Isolated Toughness Bound for Fractional(k,m)-Deleted Graphs  

作　　者：Wei GAO Wei-fan WANG Yao-jun CHEN 

机构地区：[1]School of Mathematics,Hohai University,Nanjing 210098,China [2]Department of Mathematics,Zhejiang Normal University,Jinhua 321004,China [3]Department of Mathematics,Nanjing University,Nanjing 210093,China

出　　处：《Acta Mathematicae Applicatae Sinica》2025年第1期252-269,共18页应用数学学报(英文版)

基　　金：supported by the National Science Foundation of China(Nos.12161094,12031018,11871270,12161141003and11931006).

摘　　要：A graph G is a fractional(k,m)-deleted graph if removing any m edges from G,the resulting subgraph still admits a fractional k-factor.Let k≥2 and m≥1 be integers.Denote[2m/k]^(*)=[2m/k]if 2m/k is not an integer,and[2m/k]^(*)=[2m/k]-1 if 2m/k is an integer.In this paper,we prove that G is a fractional(k,m)-deleted graph if δ(G)≥k+m and isolated toughness meets I(G)>{3-1/m,if k=2 and m≥3,k+[2m/k]^(*)m+1-[2m/k]^(*);otherwise.Furthermore,we show that the isolated toughness bound is tight.

关 键 词：GRAPH isolated toughness fractional k-factor fractional(k m)-deleted graph 

分 类 号：O157.5[理学—数学]