Deletion to Induced Matching
Akash Kumar, Mithilesh Kumar

TL;DR
This paper introduces an FPT algorithm for the Deletion to Induced Matching problem, efficiently determining if a small vertex set can partition a graph into components of size two, with extensions to exponential-time solutions.
Contribution
It presents a novel fixed-parameter tractable algorithm with a specific running time for the problem, using branch-and-reduce and path decomposition techniques.
Findings
FPT algorithm with $O^*(1.748^{k})$ running time
Extension to exact-exponential version of the problem
Effective branch-and-reduce strategy and path decomposition methods
Abstract
In the DELETION TO INDUCED MATCHING problem, we are given a graph on vertices, edges and a non-negative integer and asks whether there exists a set of vertices such that and the size of any connected component in is exactly 2. In this paper, we provide a fixed-parameter tractable (FPT) algorithm of running time 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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Taxonomy
TopicsOptimization and Search Problems · Advanced Graph Theory Research · Complexity and Algorithms in Graphs
