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A Dichotomy for Upper Domination in Monogenic Classes

  • Hassan AbouEisha
  • Shahid Hussain
  • Vadim LozinEmail author
  • Jérôme Monnot
  • Bernard Ries
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8881)

Abstract

An upper dominating set in a graph is a minimal (with respect to set inclusion) dominating set of maximum cardinality. The problem of finding an upper dominating set is NP-hard for general graphs and in many restricted graph families. In the present paper, we study the computational complexity of this problem in monogenic classes of graphs (i.e. classes defined by a single forbidden induced subgraph) and show that the problem admits a dichotomy in this family. In particular, we prove that if the only forbidden induced subgraph is a \(P_4\) or a \(2K_2\) (or any induced subgraph of these graphs), then the problem can be solved in polynomial time. Otherwise, it is NP-hard.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Hassan AbouEisha
    • 1
  • Shahid Hussain
    • 1
  • Vadim Lozin
    • 2
    Email author
  • Jérôme Monnot
    • 3
    • 4
  • Bernard Ries
    • 3
    • 4
  1. 1.King Abdullah University of Science and TechnologyThuwalSaudia Arabia
  2. 2.DIMAP and Mathematics InstituteUniversity of WarwickCoventryUK
  3. 3.PSLUniversité Paris-DauphineParis Cedex 16France
  4. 4.CNRS, LAMSADE UMR 7243ParisFrance

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