Algorithmic Aspects of Upper Domination: A Parameterised Perspective

  • Cristina Bazgan
  • Ljiljana Brankovic
  • Katrin Casel
  • Henning Fernau
  • Klaus Jansen
  • Kim-Manuel Klein
  • Michael Lampis
  • Mathieu Liedloff
  • Jérôme Monnot
  • Vangelis Th. Paschos
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9778)

Abstract

This paper studies Upper Domination, i.e., the problem of computing the maximum cardinality of a minimal dominating set in a graph, with a focus on parameterised complexity. Our main results include W[1]-hardness for Upper Domination, contrasting FPT membership for the parameterised dual Co-Upper Domination. The study of structural properties also yields some insight into Upper Total Domination. We further consider graphs of bounded degree and derive upper and lower bounds for kernelisation.

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Cristina Bazgan
    • 1
  • Ljiljana Brankovic
    • 2
    • 3
  • Katrin Casel
    • 3
  • Henning Fernau
    • 3
  • Klaus Jansen
    • 4
  • Kim-Manuel Klein
    • 4
  • Michael Lampis
    • 1
  • Mathieu Liedloff
    • 5
  • Jérôme Monnot
    • 1
  • Vangelis Th. Paschos
    • 1
  1. 1.PSL, University of Paris-Dauphine, CNRS, LAMSADE UMR 7243Paris Cedex 16France
  2. 2.School of Electrical Engineering and Computer ScienceThe University of NewcastleCallaghanAustralia
  3. 3.Fachbereich 4, InformatikwissenschaftenUniversität TrierTrierGermany
  4. 4.Institut für InformatikUniversität KielKielGermany
  5. 5.University Orléans, INSA Centre Val de Loire, LIFO EA 4022OrléansFrance

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