Maximal Induced Matchings in Triangle-Free Graphs

  • Manu Basavaraju
  • Pinar Heggernes
  • Pim van ’t Hof
  • Reza Saei
  • Yngve Villanger
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8747)

Abstract

An induced matching in a graph is a set of edges whose endpoints induce a \(1\)-regular subgraph. It is known that every \(n\)-vertex graph has at most \(10^{n/5}\approx 1.5849^n\) maximal induced matchings, and this bound is best possible. We prove that every \(n\)-vertex triangle-free graph has at most \(3^{n/3}\approx 1.4423^n\) maximal induced matchings, and this bound is attained by every disjoint union of copies of the complete bipartite graph \(K_{3,3}\). Our result implies that all maximal induced matchings in an \(n\)-vertex triangle-free graph can be listed in time \(O(1.4423^n)\), yielding the fastest known algorithm for finding a maximum induced matching in a triangle-free graph.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Manu Basavaraju
    • 1
  • Pinar Heggernes
    • 1
  • Pim van ’t Hof
    • 1
  • Reza Saei
    • 1
  • Yngve Villanger
    • 1
  1. 1.Department of InformaticsUniversity of BergenBergenNorway

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