  A \emph{matching} is a subset of edges in a graph $G$ that do not share an
endpoint. A matching $M$ is a \emph{$\mathcal{P}$-matching} if the subgraph of
$G$ induced by the endpoints of the edges of $M$ satisfies property
$\mathcal{P}$. For example, if the property $\mathcal{P}$ is that of being a
matching, being acyclic, or being disconnected, then we obtain an \emph{induced
matching}, an \emph{acyclic matching}, and a \emph{disconnected matching},
respectively. In this paper, we analyze the problems of the computation of
these matchings from the viewpoint of Parameterized Complexity with respect to
the parameter \emph{treewidth}.
