  For a nonnegative integer $k$, a graph $G$ is said to be $k$-factor-critical
if $G-Q$ admits a perfect matching for any $Q\subseteq V(G)$ with $|Q|=k$. In
this article, we prove spectral radius conditions for the existence of
$k$-factor-critical graphs. Our result generalises one previous result on
perfect matchings of graphs. Furthermore, we claim that the bounds on spectral
radius in Theorem 3.1 are sharp.
