Deletion to Induced Matching

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 $G$ 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.