An improved kernel and parameterized algorithm for deletion to induced matching

Abstract

A graph is called an induced matching if each vertex in the graph is a degree-1 vertex. The Deletion to Induced Matching problem asks whether we can delete at most k vertices from the input graph such that the remaining graph is an induced matching. This paper studies parameterized algorithms for this problem by taking the size k of the deletion set as the parameter. First, we prove a 6k-vertex kernel for this problem, improving the previous result of 7k. Second, we give an $O^{⁎}\left({1.6477}^k\right)$-time and polynomial-space algorithm, improving the previous running-time bound of $O^{⁎}\left({1.7485}^k\right)$.