On the Complexity of Minimum Maximal Uniquely Restricted Matching

Juhi Chaudhary, B. S. Panda

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

1 Scopus citations


A subset M⊆ E 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 a uniquely restricted matching if G[V(M)], the subgraph of G induced by the M-saturated vertices of G, contains exactly one perfect matching. A uniquely restricted matching M is maximal if M is not properly contained in any other uniquely restricted matching of G. Given a graph G, the Min-Max-UR Matching problem asks to find a maximal uniquely restricted matching of minimum cardinality in G. In general, the decision version of the Min-Max-UR Matching problem is known to be NP-complete for general graphs and remains so even for bipartite graphs. In this paper, we strengthen this result by proving that this problem remains NP-complete for chordal bipartite graphs and chordal graphs. On the positive side, we prove that the Min-Max-UR Matching problem is polynomial time solvable for bipartite permutation graphs and proper interval graphs. Finally, we show that the Min-Max-UR Matching problem is APX-complete for bounded degree graphs.

Original languageEnglish
Title of host publicationCombinatorial Optimization and Applications - 14th International Conference, COCOA 2020, Proceedings
EditorsWeili Wu, Zhongnan Zhang
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages13
ISBN (Print)9783030648428
StatePublished - 1 Jan 2020
Externally publishedYes
Event14th International Conference on Combinatorial Optimization and Applications, COCOA 2020 - Dallas, United States
Duration: 11 Dec 202013 Dec 2020

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12577 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference14th International Conference on Combinatorial Optimization and Applications, COCOA 2020
Country/TerritoryUnited States


  • APX-completeness
  • Graph algorithms
  • Matching
  • Minimum maximal matching
  • NP-completeness
  • Uniquely restricted matching

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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