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

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Graph-Theoretic Concepts in Computer Science: 35th International Workshop, WG 2009, Montpellier, France, June 24-26, 2009. Revised Papers

December 2009

Pages 296 - 307

https://doi.org/10.1007/978-3-642-11409-0_26

Published: 04 December 2009 Publication History

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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Kawahara JSaitoh TTakeda HYoshinaka RYoshioka Y(2023)Efficient Non-isomorphic Graph Enumeration Algorithms for Subclasses of Perfect GraphsWALCOM: Algorithms and Computation10.1007/978-3-031-27051-2_14(151-163)Online publication date: 22-Mar-2023
https://dl.acm.org/doi/10.1007/978-3-031-27051-2_14
Chakraborty SShrotri AVardi M(2019)On Symbolic Approaches for Computing the Matrix PermanentPrinciples and Practice of Constraint Programming10.1007/978-3-030-30048-7_5(71-90)Online publication date: 30-Sep-2019
https://dl.acm.org/doi/10.1007/978-3-030-30048-7_5
Dyer MJerrum MMüller H(2017)On the Switch Markov Chain for Perfect MatchingsJournal of the ACM10.1145/282232264:2(1-33)Online publication date: 30-Apr-2017
https://dl.acm.org/doi/10.1145/2822322
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Counting the Number of Matchings in Chordal and Chordal Bipartite Graph Classes

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Graph-Theoretic Concepts in Computer Science: 35th International Workshop, WG 2009, Montpellier, France, June 24-26, 2009. Revised Papers

December 2009

352 pages

ISBN:9783642114083

Editors:
Christophe Paul
CNRS - LIRMM, Montpellier Cedex 5, France 34392
,
Michel Habib
LIAFA, case 7014, Université Paris Diderot, Paris Cedex 13, France 75205

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Springer-Verlag

Berlin, Heidelberg

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Published: 04 December 2009

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Kawahara JSaitoh TTakeda HYoshinaka RYoshioka Y(2023)Efficient Non-isomorphic Graph Enumeration Algorithms for Subclasses of Perfect GraphsWALCOM: Algorithms and Computation10.1007/978-3-031-27051-2_14(151-163)Online publication date: 22-Mar-2023
https://dl.acm.org/doi/10.1007/978-3-031-27051-2_14
Chakraborty SShrotri AVardi M(2019)On Symbolic Approaches for Computing the Matrix PermanentPrinciples and Practice of Constraint Programming10.1007/978-3-030-30048-7_5(71-90)Online publication date: 30-Sep-2019
https://dl.acm.org/doi/10.1007/978-3-030-30048-7_5
Dyer MJerrum MMüller H(2017)On the Switch Markov Chain for Perfect MatchingsJournal of the ACM10.1145/282232264:2(1-33)Online publication date: 30-Apr-2017
https://dl.acm.org/doi/10.1145/2822322
Dyer MJerrum MMüller H(2016)On the switch markov chain for perfect matchingsProceedings of the twenty-seventh annual ACM-SIAM symposium on Discrete algorithms10.5555/2884435.2884573(1972-1983)Online publication date: 10-Jan-2016
https://dl.acm.org/doi/10.5555/2884435.2884573
Djelloul S(2014)Solving Matching Problems Efficiently in Bipartite GraphsCombinatorial Algorithms10.1007/978-3-319-19315-1_12(128-139)Online publication date: 15-Oct-2014
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Kijima SOkamoto YUno T(2011)Dominating set counting in graph classesProceedings of the 17th annual international conference on Computing and combinatorics10.5555/2033094.2033096(13-24)Online publication date: 14-Aug-2011
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de Menibus BUno T(2011)Maximal matching and path matching counting in polynomial time for graphs of bounded clique widthProceedings of the 8th annual conference on Theory and applications of models of computation10.5555/2008967.2009031(483-494)Online publication date: 23-May-2011
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Reconfiguration graphs for vertex colourings of chordal and chordal bipartite graphs

Connected matchings in chordal bipartite graphs

Representation characterizations of chordal bipartite graphs

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