Abstract:  A graph G is called a fractional(g,f,m)-deleted graph if the resulting graph admits a fractional(g,f)-factor after any medges are deleted.In this paper,we prove that if Gis a graph of order n,1≤a ≤g(x)≤f(x)-Δ≤b-Δ for any x∈V(G),δ(G)≥(b-Δ)(b+1)/a+2m,n≥(a+b)(2(a+b)+2m-1)/(a+Δ), and|NG(x1)∪NG(x2)|≥(b-Δ)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

Key words: Graph, Neighborhood union condition, Fractional deleted graph