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On the vertices belonging to all, some, none minimum dominating set
Discrete Applied Mathematics ( IF 1.1 ) Pub Date : 2021-01-01 , DOI: 10.1016/j.dam.2020.08.020
Valentin Bouquet , François Delbot , Christophe Picouleau

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.

中文翻译:

在属于所有、一些、非最小支配集的顶点上

我们刻画了属于所有最小支配集、某些最小支配集但不是全部、以及不属于任何最小支配集的顶点。我们为一些经过充分研究的图子类改进了这种表征:弦、无爪、无三角形。我们还展示了一些图表,回答了关于最小支配集的文献中的一些开放问题。
更新日期:2021-01-01
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