Parameterized Results on Acyclic Matchings with Implications for Related Problems

Juhi Chaudhary, Meirav Zehavi

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Scopus citations

Abstract

A matching M in a graph G is an acyclic matching if the subgraph of G induced by the endpoints of the edges of M is a forest. Given a graph G and a positive integer l, Acyclic Matching asks whether G has an acyclic matching of size (i.e., the number of edges) at least l. In this paper, we first prove that assuming (Formula presented), there does not exist any FPT-approximation algorithm for Acyclic Matching that approximates it within a constant factor when parameterized by l. Our reduction is general in the sense that it also asserts FPT-inapproximability for Induced Matching and Uniquely Restricted Matching. We also consider three below-guarantee parameters for Acyclic Matching, viz. (Formula presented), where n is the number of vertices in G, MM(G) is the matching number of G, and IS(G) is the independence number of G. We note that the result concerning the below-guarantee parameter n/2-l is the most technical part of our paper. Also, we show that Acyclic Matching does not exhibit a polynomial kernel with respect to vertex cover number (or vertex deletion distance to clique) plus the size of the matching unless (Formula presented).

Original languageEnglish
Title of host publicationGraph-Theoretic Concepts in Computer Science - 49th International Workshop, WG 2023, Revised Selected Papers
EditorsDaniël Paulusma, Bernard Ries
PublisherSpringer Science and Business Media Deutschland GmbH
Pages201-216
Number of pages16
ISBN (Print)9783031433795
DOIs
StatePublished - 1 Jan 2023
Event49th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2023 - Fribourg, Switzerland
Duration: 28 Jun 202330 Jun 2023

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume14093 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference49th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2023
Country/TerritorySwitzerland
CityFribourg
Period28/06/2330/06/23

Keywords

  • Acyclic Matching
  • Induced Matching
  • Kernelization Lower Bounds
  • Parameterized Algorithms
  • Uniquely Restricted Matching

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science

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