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Enumerating Minimal Dominating Sets in Triangle-Free Graphs

Authors Marthe Bonamy, Oscar Defrain, Marc Heinrich, Jean-Florent Raymond



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Author Details

Marthe Bonamy
  • CNRS, Université de Bordeaux, France
Oscar Defrain
  • LIMOS, Université Clermont Auvergne, France
Marc Heinrich
  • LIRIS, Université Claude-Bernard, Lyon, France
Jean-Florent Raymond
  • LaS team, Technische Universität Berlin, Germany

Acknowledgements

The authors wish to thank Paul Ouvrard for extensive discussions on the topic of this paper. We also gratefully acknowledge support from Nicolas Bonichon and the Simon family for the organization of the 3^{rd} Pessac Graph Workshop, where this research was done. Last but not least, we thank Peppie for her unwavering support during the work sessions.

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Marthe Bonamy, Oscar Defrain, Marc Heinrich, and Jean-Florent Raymond. Enumerating Minimal Dominating Sets in Triangle-Free Graphs. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 16:1-16:12, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2019)
https://doi.org/10.4230/LIPIcs.STACS.2019.16

Abstract

It is a long-standing open problem whether the minimal dominating sets of a graph can be enumerated in output-polynomial time. In this paper we prove that this is the case in triangle-free graphs. This answers a question of Kanté et al. Additionally, we show that deciding if a set of vertices of a bipartite graph can be completed into a minimal dominating set is a NP-complete problem.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph algorithms
  • Theory of computation → Design and analysis of algorithms
Keywords
  • Enumeration algorithms
  • output-polynomial algorithms
  • minimal dominating set
  • triangle-free graphs
  • split graphs

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