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International Workshop on Graph-Theoretic Concepts in Computer Science

WG 2015: Graph-Theoretic Concepts in Computer Science pp 138–153Cite as

A Polynomial Delay Algorithm for Enumerating Minimal Dominating Sets in Chordal Graphs

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9224))

Abstract

An output-polynomial algorithm for the listing of minimal dominating sets in graphs is a challenging open problem and is known to be equivalent to the well-known Transversal problem which asks for an output-polynomial algorithm for listing the set of minimal transversals in hypergraphs. We give a polynomial delay algorithm to list the set of minimal dominating sets in chordal graphs, an important and well-studied graph class where such an algorithm was not known. The algorithm uses a new decomposition method of chordal graphs based on clique trees.

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Author information

Authors and Affiliations

  1. Clermont-Université, Université Blaise Pascal, LIMOS, CNRS, Clermont-Ferrand, France

    Mamadou Moustapha Kanté, Vincent Limouzy & Lhouari Nourine

  2. Université Claude Bernard Lyon 1, LBBE, CNRS, Villeurbanne, France

    Arnaud Mary

  3. National Institute of Informatics, Tokyo, Japan

    Takeaki Uno

Authors
  1. Mamadou Moustapha Kanté
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  2. Vincent Limouzy
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  3. Arnaud Mary
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  4. Lhouari Nourine
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  5. Takeaki Uno
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Corresponding author

Correspondence to Mamadou Moustapha Kanté .

Editor information

Editors and Affiliations

  1. TU München Institut für Informatik, Garching, Germany

    Ernst W. Mayr

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Kanté, M.M., Limouzy, V., Mary, A., Nourine, L., Uno, T. (2016). A Polynomial Delay Algorithm for Enumerating Minimal Dominating Sets in Chordal Graphs. In: Mayr, E. (eds) Graph-Theoretic Concepts in Computer Science. WG 2015. Lecture Notes in Computer Science(), vol 9224. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53174-7_11

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  • DOI: https://doi.org/10.1007/978-3-662-53174-7_11

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-53173-0

  • Online ISBN: 978-3-662-53174-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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