In the DELETION TO INDUCED MATCHING problem, we are given a graph $G$ on $n$ vertices, $m$ edges and a non-negative integer $k$ and asks whether there exists a set of vertices $S \subseteq V(G) $ such that $|S|\le k$ and the size of any connected component in $G-S$ is exactly 2. In this paper, we provide a fixed-parameter tractable (FPT) algorithm of running time $O^*(1.748^{k})$ for the DELETION TO INDUCED MATCHING problem using branch-and-reduce strategy and path decomposition. We also extend our work to the exact-exponential version of the problem.

中文翻译：

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删除到诱导匹配

在 DELETION TO INDUCED MATCHING 问题中，我们给出了一个在 $n$ 个顶点、$m$ 条边和一个非负整数 $k$ 上的图 $G$，并询问是否存在一组顶点 $S \subseteq V( G) $ 使得 $|S|\le k$ 和 $GS$ 中任意连通分量的大小恰好为 2。 在本文中，我们提供了运行时间 $O^* 的固定参数易处理 (FPT) 算法(1.748^{k})$ 用于使用分支和归约策略和路径分解的 DELETION TO INDUCED MATCHING 问题。我们还将我们的工作扩展到问题的精确指数版本。