A spectral condition for graphs with all fractional $[a,b]$-factors

Jiaxin Zheng, Junjie Wang

Published 2022-12-07Version 1

Let $a<b$ be two positive integers. We say that a graph $G$ has all fractional $[a,b]$-factors if it has a fractional $p$-factor for every $p: V(G) \rightarrow \mathbb{Z}^+$ such that $a\le p(x)\le b$ for every $x\in V(G)$. In this paper, we provide a tight spectral radius condition for graphs having all fractional $[a,b]$-factors.