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Journal Articles Discrete Applied Mathematics Year : 2021

On the vertices belonging to all, some, none minimum dominating set

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Abstract

We characterize the vertices belonging to all minimum dominating sets, to some minimum dominating sets but not all, and to no minimum dominating set. We refine this characterization for some well studied sub-classes of graphs: chordal, claw-free, triangle-free. Also we exhibit some graphs answering to some open questions of the literature on minimum dominating sets.
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Dates and versions

hal-02434684 , version 1 (17-01-2020)

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Valentin Bouquet, François Delbot, Christophe Picouleau. On the vertices belonging to all, some, none minimum dominating set. Discrete Applied Mathematics, 2021, 288, pp.9-19. ⟨10.1016/j.dam.2020.08.020⟩. ⟨hal-02434684⟩
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