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International Symposium on Fundamentals of Computation Theory

FCT 2011: Fundamentals of Computation Theory pp 298–309Cite as

Enumeration of Minimal Dominating Sets and Variants

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6914))

Abstract

In this paper, we are interested in the enumeration of minimal dominating sets in graphs. A polynomial delay algorithm with polynomial space in split graphs is presented. We then introduce a notion of maximal extension (a set of edges added to the graph) that keeps invariant the set of minimal dominating sets, and show that graphs with extensions as split graphs are exactly the ones having chordal graphs as extensions. We finish by relating the enumeration of some variants of dominating sets to the enumeration of minimal transversals in hypergraphs.

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Author information

Authors and Affiliations

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

    Mamadou Moustapha Kanté, Vincent Limouzy, Arnaud Mary & Lhouari Nourine

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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Editor information

Editors and Affiliations

  1. Department of Informatics, University of Oslo, Postboks 1080 Blindern, 0316, Oslo, Norway

    Olaf Owe  & Martin Steffen  & 

  2. Department of Informatics, University of Bergen, Postboks 7800, 5020, Bergen, Norway

    Jan Arne Telle

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Kanté, M.M., Limouzy, V., Mary, A., Nourine, L. (2011). Enumeration of Minimal Dominating Sets and Variants. In: Owe, O., Steffen, M., Telle, J.A. (eds) Fundamentals of Computation Theory. FCT 2011. Lecture Notes in Computer Science, vol 6914. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22953-4_26

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  • DOI: https://doi.org/10.1007/978-3-642-22953-4_26

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22952-7

  • Online ISBN: 978-3-642-22953-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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