Acyclic Matching in Some Subclasses of Graphs

B. S. Panda, Juhi Chaudhary

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

7 Scopus citations

Abstract

A subset (Formula Presented) of edges of a graph G = (V, E) is called a matching if no two edges of M share a common vertex. A matching M in a graph G is called an acyclic matching if G[V (M)], the subgraph of G induced by the M-saturated vertices of G is acyclic. The Acyclic Matching Problem is the problem of finding an acyclic matching of maximum size. The decision version of the Acyclic Matching Problem is known to be NP-complete for general graphs as well as for bipartite graphs. In this paper, we strengthen this result by showing that the decision version of the Acyclic Matching Problem remains NP-complete for comb-convex bipartite graphs and dually-chordal graphs. On the positive side, we present linear time algorithms to compute an acyclic matching of maximum size in split graphs and proper interval graphs. Finally, we show that the Acyclic Matching Problem is hard to approximate within a factor of n1−ɛ for any ɛ > 0, unless P = NP and the Acyclic Matching Problem is APX-complete for 2k + 1-regular graphs for k ≥ 3, where k is a constant.

Original languageEnglish
Title of host publicationCombinatorial Algorithms - 31st International Workshop, IWOCA 2020, Proceedings
EditorsLeszek Gasieniec, Leszek Gasieniec, Ralf Klasing, Tomasz Radzik
PublisherSpringer
Pages409-421
Number of pages13
ISBN (Print)9783030489656
DOIs
StatePublished - 1 Jan 2020
Externally publishedYes
Event31st International Workshop on Combinatorial Algorithms, IWOCA 2020 - Bordeaux, France
Duration: 8 Jun 202010 Jun 2020

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12126 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference31st International Workshop on Combinatorial Algorithms, IWOCA 2020
Country/TerritoryFrance
CityBordeaux
Period8/06/2010/06/20

Keywords

  • Approximation algorithm
  • Bipartite graphs
  • Chordal graphs
  • Graph algorithm
  • Matching
  • NP-completeness

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science

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