An improved kernel and parameterized algorithm for deletion to induced matching

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 th...

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Bibliographic Details
Published in:Theoretical computer science Vol. 1041; p. 115215
Main Authors: Liu, Yuxi, Xiao, Mingyu
Format: Journal Article
Language:English
Published: Elsevier B.V 07.07.2025
Subjects:
Graph algorithms
Linear kernel
Maximum induced matching
Parameterized algorithms
Parameterized algorithms
Graph algorithms
Maximum induced matching
Linear kernel
ISSN:0304-3975
Online Access:Get full text
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Summary: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).
ISSN:0304-3975
DOI:10.1016/j.tcs.2025.115215