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Counting the Number of Matchings in Chordal and Chordal Bipartite Graph Classes

  • Yoshio Okamoto
  • Ryuhei Uehara
  • Takeaki Uno
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5911)

Abstract

We provide polynomial-time algorithms for counting the number of perfect matchings in chain graphs, cochain graphs, and threshold graphs. These algorithms are based on newly developed subdivision schemes that we call a recursive decomposition. On the other hand, we show the \(\sharp\) P-completeness for counting the number of perfect matchings in chordal graphs, split graphs and chordal bipartite graphs. This is in an interesting contrast with the fact that counting the number of independent sets in chordal graphs can be done in linear time.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Yoshio Okamoto
    • 1
  • Ryuhei Uehara
    • 2
  • Takeaki Uno
    • 3
  1. 1.Graduate School of Information Science and EngineeringTokyo Institute of TechnologyTokyoJapan
  2. 2.School of Information ScienceJAISTIshikawaJapan
  3. 3.National Institute of InformaticsTokyoJapan

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