Exponential Time Algorithms for the Minimum Dominating Set Problem on Some Graph Classes

  • Serge Gaspers
  • Dieter Kratsch
  • Mathieu Liedloff
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4059)


The Minimum Dominating Set problem remains NP-hard when restricted to chordal graphs, circle graphs and c-dense graphs (i.e. |E| ≥cn 2 for a constant c, 0<c<1/2). For each of these three graph classes we present an exponential time algorithm solving the Minimum Dominating Set problem. The running times of those algorithms are O(1.4173 n ) for chordal graphs, O(1.4956 n ) for circle graphs, and \(O(1.2303^{(1+\sqrt{1-2c})n})\) for c-dense graphs.


Input Graph Tree Decomposition Domination Number Chordal Graph Graph Class 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Serge Gaspers
    • 1
  • Dieter Kratsch
    • 2
  • Mathieu Liedloff
    • 2
  1. 1.Department of InformaticsUniversity of BergenBergenNorway
  2. 2.LITA, Université de Paul Verlaine – MetzMetzFrance

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