Abstract
Let a and b be two positive integers with with \(1\le a\le b\) and \(b\ge 2\), and let G be a graph of order \(n\ge \frac{(a+b-3)(2a+b-1)-a+1}{a}\). We say that G has all fractional [a, b]-factors if G has a fractional r-factor for any integer r with \(a\le r\le b\). In this paper, we testify that \(G-I\) has all fractional [a, b]-factors for any independent set I of G if \(\delta (G)\ge \frac{(a+b-1)n+a+b-1}{2a+b-1}\) and \(\delta (G)>\frac{(a+b-2)n+2\alpha (G)-1}{2a+b-2}\). Furthermore, the result in Theorem 1 is sharp.
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Communicated by Sharad S Sane
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Sun, Z., Zhou, S. Nash-Williams conditions for the existence of all fractional [a, b]-factors. Indian J Pure Appl Math 52, 542–547 (2021). https://doi.org/10.1007/s13226-021-00054-3
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DOI: https://doi.org/10.1007/s13226-021-00054-3