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International Workshop on Graph-Theoretic Concepts in Computer Science

WG 2017: Graph-Theoretic Concepts in Computer Science pp 289–302Cite as

Enumeration and Maximum Number of Maximal Irredundant Sets for Chordal Graphs

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10520))

Abstract

In this paper we provide exponential-time algorithms to enumerate the maximal irredundant sets of chordal graphs and two of their subclasses. We show that the maximum number of maximal irredundant sets of a chordal graph is at most \(1.7549^n\), and these can be enumerated in time \(O(1.7549^n)\). For interval graphs, we achieve the better upper bound of \(1.6957^n\) for the number of maximal irredundant sets and we show that they can be enumerated in time \(O(1.6957^n)\). Finally, we show that forests have at most \(1.6181^n\) maximal irredundant sets that can be enumerated in time \(O(1.6181^n)\). We complement the latter result by providing a family of forests having at least \(1.5292^n\) maximal irredundant sets.

This work is supported by the Research Council of Norway by the CLASSIS project and the French National Research Agency by the ANR project GraphEn (ANR-15-CE40-0009).

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Author information

Authors and Affiliations

  1. Department of Informatics, University of Bergen, Bergen, Norway

    Petr A. Golovach

  2. LITA, Université de Lorraine, Metz, France

    Dieter Kratsch & Mohamed Yosri Sayadi

  3. INSA Centre Val de Loire, LIFO EA 4022, Université d’Orléans, 45067, Orléans, France

    Mathieu Liedloff

Authors
  1. Petr A. Golovach
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  2. Dieter Kratsch
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  3. Mathieu Liedloff
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  4. Mohamed Yosri Sayadi
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Corresponding author

Correspondence to Petr A. Golovach .

Editor information

Editors and Affiliations

  1. Utrecht University, Utrecht, The Netherlands

    Hans L. Bodlaender

  2. Rheinisch-Westfälische Technische Hochschule Aachen, Aachen, Germany

    Gerhard J. Woeginger

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Golovach, P.A., Kratsch, D., Liedloff, M., Sayadi, M.Y. (2017). Enumeration and Maximum Number of Maximal Irredundant Sets for Chordal Graphs. In: Bodlaender, H., Woeginger, G. (eds) Graph-Theoretic Concepts in Computer Science. WG 2017. Lecture Notes in Computer Science(), vol 10520. Springer, Cham. https://doi.org/10.1007/978-3-319-68705-6_22

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  • DOI: https://doi.org/10.1007/978-3-319-68705-6_22

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  • Print ISBN: 978-3-319-68704-9

  • Online ISBN: 978-3-319-68705-6

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