A New Sufficient Condition for Graphs to Have (g, f)-Factors

Let a and b be integers such that 1 <= a < b, and let G be a graph of order n with n > (a+b)(2a+2b-3)/a+1, and the minimum degree delta(G) >= and (b-1)(2) - (a+1)(b-a-2)/a+1, let g(x) and (x) be two nonnegative integer-valued functions defined on V(G) such that a <= g(x) < f (x) <= b for each x is an element of V(G). We prove that if vertical bar N-G(x) boolean OR N-G(y)vertical bar >= (b-1)n/a+b for any two nonadjacent vertices x and y in G, then G has a (g, f)-factor. Furthermore, it is showed that the result in this paper is best possible in some sense.