A note on locating-dominating sets in twin-free graphs

A note on locating-dominating sets in twin-free graphs

In this short note, we prove that every twin-free graph on n vertices contains a locating-dominating set of size at most ⌈58n⌉. This improves the earlier bound of ⌊23n⌋ due to Foucaud, Henning, Löwenstein and Sasse from 2016, and makes some progress towards the well-studied locating-dominating conje...

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Veröffentlicht in:Discrete mathematics 2025-02, Vol.348 (2), p.114297, Article 114297
Hauptverfasser: Bousquet, Nicolas, Chuet, Quentin, Falgas–Ravry, Victor, Jacques, Amaury, Morelle, Laure
Format: Artikel
Sprache:eng
Schlagworte:
Graph partitions
Locating sets
Locating-dominating sets
Twin-free graphs
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Zusammenfassung:In this short note, we prove that every twin-free graph on n vertices contains a locating-dominating set of size at most ⌈58n⌉. This improves the earlier bound of ⌊23n⌋ due to Foucaud, Henning, Löwenstein and Sasse from 2016, and makes some progress towards the well-studied locating-dominating conjecture of Garijo, González and Márquez.
ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2024.114297