Enumerating Minimal Dominating Sets in Triangle-Free Graphs

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.
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Marthe Bonamy, Oscar Defrain, Marc Heinrich, Jean-Florent Raymond. Enumerating Minimal Dominating Sets in Triangle-Free Graphs. Leibniz International Proceedings in Informatics , Leibniz-Zentrum für Informatik, 2019, ⟨10.4230/LIPIcs.STACS.2019.16⟩. ⟨hal-02181721⟩

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