Some sufficient conditions for graphs to have (g,f)-factors

Suppose that G is a graph with vertex set V(G) and edge set E(G), and let g and f be two non-negative integer-valued functions defined on V(G) such that g(x) <= f(x) for each x is an element of V(G). A (g, f)-factor of G is a spanning subgraph F of G such that g(x) <= d(F)(X) <= f(x) for each x is an element of V(F). In this paper, some sufficient conditions for a graph to have a (g, f)-factor are given.