  Let $\gamma(G)$ be the domination number of a graph $G$. A graph $G$ is
\emph{domination-vertex-critical}, or \emph{$\gamma$-vertex-critical}, if
$\gamma(G-v)< \gamma(G)$ for every vertex $v \in V(G)$. In this paper, we show
that: Let $G$ be a $\gamma$-vertex-critical graph and $\gamma(G)=3$. (1) If $G$
is of even order and $K_{1,6}$-free, then $G$ has a perfect matching; (2) If
$G$ is of odd order and $K_{1,7}$-free, then $G$ has a near perfect matching
with only three exceptions. All these results improve the known results.
