On all fractional [a, b]-factors

Abstract

Let a and 6 be two positive integers with 2 ≤ a ≤ 6, and let G be a graph of order n with n ≥(2a+b)(a+b-2)/a, Let h : E{G) → [0,1] be a function. If a ≤∑ex h(e) ≤ b holds for any x V(G), then we call G[Fh] a fractional [a,b]-factor of G with indicator function h where Fh = {e E(G): h(e) >0}. We say that G has all fractional [a, b]-factors if G has a fractional r-factor for every r : V{G) → Z⁺ satisfying a ≤ r(x) ≤ b for any x V(G). In this paper, it is proved that G - I has all fractional [a, b]-factors for any independent set I of G if bind(G) ≥ 2 + b-1/a and δ(G) > (a+b-1)n+a+b-2/2a+b-1. © 2018 Utilitas Mathematica Publishing Inc. All rights reserved.