Abstract

A (g, f)-factor of a graph is a subset F of E such that for all v ∈ V, g(v) ≤ degF(v) ≤ f(v). Lovasz gave a necessary and sufficient condition for the existence of a (g, f)-factor. We extend, to the case of edge-weighted graphs, a result of Kano and Saito who showed that if g(v) < λdegE(v) < f(v) for any λ ∈ [0,1], then a (g, f)-factor always exist. In addition, we use results of Anstee to provide new necessary and sufficient conditions for the existence of a (g, f)-factor. © 2008 Wiley Periodicals, Inc.