On the Complexity of Minimum Maximal Acyclic Matchings

Juhi Chaudhary, Sounaka Mishra, B. S. Panda

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


Given a graph G, Min-Max-Acy-Matching is the problem of finding a maximal matching M in G of minimum cardinality such that the set of M-saturated vertices induces an acyclic subgraph in G. Min-Max-Acy-Matching is known to be NP -hard. In this paper, we strengthen this result by proving that the decision version of Min-Max-Acy-Matching is NP -complete for planar perfect elimination bipartite graphs. We also prove that Min-Max-Acy-Matching for bipartite graphs cannot be approximated within a ratio of n1 - ϵ, for any ϵ> 0 unless P= NP. Finally, we show that Min-Max-Acy-Matching is APX -hard for 4-regular graphs.

Original languageEnglish
Title of host publicationComputing and Combinatorics - 28th International Conference, COCOON 2022, Proceedings
EditorsYong Zhang, Dongjing Miao, Rolf Möhring
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages12
ISBN (Print)9783031221040
StatePublished - 1 Jan 2022
Event28th International Conference on Computing and Combinatorics, COCOON 2022 - Shenzhen, China
Duration: 22 Oct 202224 Oct 2022

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume13595 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference28th International Conference on Computing and Combinatorics, COCOON 2022


  • Acyclic matching
  • APX -hardness
  • Matching
  • Minimum maximal acyclic matching
  • NP -completeness

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)


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