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Enumerating Minimal Dominating Sets in Triangle-Free Graphs

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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.

BibTeX - Entry

@InProceedings{bonamy_et_al:LIPIcs:2019:10255,
  author =	{Marthe Bonamy and Oscar Defrain and Marc Heinrich and Jean-Florent Raymond},
  title =	{{Enumerating Minimal Dominating Sets in Triangle-Free Graphs}},
  booktitle =	{36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
  pages =	{16:1--16:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-100-9},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{126},
  editor =	{Rolf Niedermeier and Christophe Paul},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/10255},
  doi =		{10.4230/LIPIcs.STACS.2019.16},
  annote =	{Keywords: Enumeration algorithms, output-polynomial algorithms, minimal dominating set, triangle-free graphs, split graphs}
}

Keywords: Enumeration algorithms, output-polynomial algorithms, minimal dominating set, triangle-free graphs, split graphs
Seminar: 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)
Issue date: 2019
Date of publication: 2019


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