Binding numbers and fractional (g, f)-deleted graphs

Let G be a graph, and let g, f be two nonnegative integer-valued functions defined on V(G) such that g(x) <= f(x) for all x is an element of V(G). For x is an element of V(G), E(x) denotes the set of edges incident with x. A fractional (g, f)-factor is a function h that assigns to each edge of a graph G a number in [0,1], so that for each vertex x we have g(x) <= d(G)(h)(x) <= f(x), where d(G)(h)(x) = Sigma(e is an element of(x)) h(e) is the fractional degree of x in G. A graph G is called a fractional (g, f)-deleted graph if G - e has a fractional (g, f)-factor for any e is an element of E(G). In this paper we use binding numbers to obtain two sufficient conditions for a graph to be a fractional (g, f)-deleted graph. Furthermore, these results are shown to be best possible in some sense.