  Let $G$ be a connected simple graph of order $n$ and let $\Delta(G)$ and
$\chi'(G)$ denote the maximum degree and chromatic index of $G$, respectively.
Vizing proved that $\chi'(G)=\Delta(G)$ or $\Delta(G)+1$. Following this
result, $G$ is called $\Delta$-critical if $\chi'(G)=\Delta(G)+1$ and
$\chi'(G-e)=\Delta(G)$ for every $e\in E(G)$. In 1968, Vizing conjectured that
if $G$ is an $n$-vertex $\Delta$-critical graph, then the independence number
$\alpha(G)\le n/2$. Furthermore, he conjectured that, in fact, $G$ has a
2-factor. Luo and Zhao showed that if $G$ is an $n$-vertex $\Delta$-critical
graph with $\Delta(G)\ge n/2$, then $\alpha(G)\le n/2$. More recently, they
showed that if $G$ is an $n$-vertex $\Delta$-critical graph with $\Delta(G)\ge
6n/7$, then $G$ has a hamiltonian cycle, and so $G$ has a 2-factor. In this
paper, we show that if $G$ is an $n$-vertex $\Delta$-critical graph with
$\Delta(G)\ge n/2$, then $G$ has a 2-factor.
