Deletion to Induced Matching

08/21/2020 ∙ by Akash Kumar, et al. ∙ 0

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 ⊆ V(G) such that |S|≤ 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.



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