分数(g,f,m)-消去图的不相邻顶点领域并条件

摘要

一个图称为分数(g,f,m)-消去图若删除任意m条边后的剩余子图依然存在分数(g,f)-因子.本文证明若图G的阶为n,1≤a≤g(z)≤f(x)-△≤b-△对任意顶点x∈V(G)成立,δ(G)≥(b-△)(b+1)/a+2m,n≥(a+b)(2(a+ b)+2m-1)/a+△,且| NG(x1) U NG(x2)|≥(b-△)n/a+b对任意不相邻顶点x1和x2都成立,则G是分数(g,f,m)-消去图.这个领域并条件在一定程度上是最好的.%A graph G is called a fractional (g,f,m) -deleted graph if the resulting graph admits a fractional (g,f)-factor after any m edges are deleted.In this paper,we prove that if G is a graph of order n,1 ≤ a ≤g(x) ≤ f(x)-△ ≤ b-△ for any x ∈ V(G),δ(G) ≥(b-△)(b+1)/a+ 2m,n ≥(a +b)(2(a +b) + 2m-1)/a+△,and |NG(x1) U NG(x2) |≥(b-△)n/a+b for any non-adjacent vertices x1 and x2,then G is a fractional (g,f,m)-deleted graph.The result is tight on the neighborhood union condition in some sense.