A note on fractional (g, f, m)-deleted graphs

A graph G is called a fractional (g, f, m)-deleted graph if after deleting any m edges then the resulting graph admits a fractional (g, f)-factor. In this paper, we prove that if G is a graph of order n, and if 1 <= a <= g(x) < f(x) <= b for any x is an element of V(G), delta(G) >= b(2)(i-1)/a + 2m, n > (a+b)(i(a+b)+2m-2)/a, and vertical bar N-G(x(1)) boolean OR N-G(x(2)) boolean OR ... boolean OR N-G(x(i))vertical bar >= bn/a+b for any independent set {x(1), x(2), ... , x(i)} of V(G), where i >= 2, then G is a fractional (g, f, m)-deleted graph. The result is tight on the neighborhood union condition.