An improved kernel and parameterized algorithm for deletion to induced matching - Liu, Yuxi; Xiao, Mingyu (Theoretical computer science, 2025)
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⁎(1.6477k)-time and polynomial-space algorithm, improving the previous running-time bound of O⁎(1.7485k).