| Issue |
RAIRO-Oper. Res.
Volume 58, Number 3, May-June 2024
|
|
|---|---|---|
| Page(s) | 2631 - 2636 | |
| DOI | https://doi.org/10.1051/ro/2024108 | |
| Published online | 25 June 2024 | |
Graphs obtained by disjoint unions and joins of cliques and stable sets
Polytechnique Montréal and GERAD, Department of Mathematics and Industrial Engineering, Montréal, Canada
* Corresponding author: alain.hertz@gerad.ca
Received:
28
December
2023
Accepted:
10
May
2024
We consider the set of graphs that can be constructed from a one-vertex graph by repeatedly adding a clique or a stable set linked to all or none of the vertices added in previous steps. This class of graphs contains various well-studied graph families such as threshold, domishold, co-domishold and complete multipartite graphs, as well as graphs with linear clique-width at most 2. We show that it can be characterized by three forbidden induced subgraphs as well as by properties involving maximal stable sets and minimal dominating sets. We also give a simple recognition algorithm and formulas for the computation of the stability and domination numbers of these graphs.
Mathematics Subject Classification: 05C75 / 90C27
Key words: Disjoint union and join of graphs / cliques / stable sets / dominating sets
© The authors. Published by EDP Sciences, ROADEF, SMAI 2024
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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