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}.

翻译：\textbf{匹配}是图$G$中边的一个子集，其中任意两条边没有公共端点。若匹配$M$的端点在图$G$中导出的子图满足性质$\mathcal{P}$，则称$M$为\textbf{$\mathcal{P}$-匹配}。例如，当性质$\mathcal{P}$分别为匹配性、无环性或非连通性时，我们分别得到\textbf{诱导匹配}、\textbf{无环匹配}和\textbf{非连通匹配}。本文从参数\textbf{树宽}的参数化复杂性角度分析这些匹配的计算问题。