On(g, f)-Factorizations of Graghs

Let G be a graph and g, f be two nonnegative integer-valued functions defined on thevertices set V(G) of G and g≤f, A (g, f)-factor of a graph G is a spanning subgraph F of G such that g(x)≤d_F(x)≤f(x) for all x∈V(G). If G itself is a (g, f)-factor, then itis said that G is a (g, f)-graph. If the edges of G can be decomposed into some edgedisjoint (g, f)-factors, then it is called that G is (g, f)-factorable. In this paper, onesufficient condition for a graph to be (g, f)-factorable is given.