ON (G,F)-FACTORIZATIONS OF GRAPHS

Let G be a graph and g, f be two nonnegative integer-valued functions defined on the vertices set V(G) of G and g less than or equal to f. A (g, f)-factor of a graph G is a spanning subgraph F of G such that g( x)less than or equal to d(F)(x)less than or equal to f(x) for all x is an element of V(G). If G itself is a (g, f)-factor, then it is said t hat G is a (g, f)-graph. If the edges of G can be decomposed into some edge disjoint (g, f)-factors, then it is called that G is (g, f)-fact orable. In this paper, one sufficient condition for a graph to be (g, f)-factorable is given.