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

Abstract

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 ε V(G). For x ε; 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^h_G(x) ≤ f(x), where d^h_G(x) =J2e£E(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 € 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.