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Deletion to Induced Matching (2008.09660v2)
Published 21 Aug 2020 in cs.DS, cs.CC, and cs.DM
Abstract: 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.