The existence of all fractional [a, 6]-factors in networks

Abstract

Let a and b be two positive integers with a < b, and let G a graph of order n > [a+b-Wa+b-ij-A+1) and left I be an independent set of G. In this paper, we prove that G - I has all fractional [a,fc]-factors if G satisfies δ <[a+b-1)n+1a-1/2a+b-1 Ng(X)≥[a+b-1)n+2a+b-1/a+b-1(X)-(a+1)/2a+b-1 for every nonempty independent subset X of V(G). Furthermore, it is shown that the result is sharp. © 2018 Utilitas Mathematica Publishing Inc. All rights reserved.