  For a matching $M$ in a graph $G$, let $G(M)$ be the subgraph of $G$ induced
by the vertices of $G$ that are incident with an edge in $M$. The matching $M$
is induced, if $G(M)$ is $1$-regular, and $M$ is uniquely restricted, if $M$ is
the unique perfect matching of $G(M)$. The induced matching number $\nu_s(G)$
of $G$ is the largest size of an induced matching in $G$, and the uniquely
restricted matching number $\nu_{ur}(G)$ of $G$ is the largest size of a
uniquely restricted matching in $G$.
  Golumbic, Hirst, and Lewenstein (Uniquely restricted matchings, Algorithmica
31 (2001) 139-154) posed the problem to characterize the graphs $G$ with
$\nu_s(G)=\nu_{ur}(G)$. We give a complete characterization of the
$2$-connected subcubic graphs $G$ of sufficiently large order with
$\nu_s(G)=\nu_{ur}(G)$. As a consequence, we are able to show that the subcubic
graphs $G$ with $\nu_s(G)=\nu_{ur}(G)$ can be recognized in polynomial time.
