English

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

Combinatorics 2021-12-14 v1 Discrete Mathematics

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.

Keywords

Cite

@article{arxiv.1909.02843,
  title  = {On the vertices belonging to all, some, none minimum dominating set},
  author = {Valentin Bouquet and François Delbot and Christophe Picouleau},
  journal= {arXiv preprint arXiv:1909.02843},
  year   = {2021}
}

Comments

11 figures