A note on locating-dominating sets in twin-free graphs
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909378734456832 |
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| author | Bousquet, Nicolas Chuet, Quentin Falgas-Ravry, Victor Jacques, Amaury Morelle, Laure |
| author_facet | Bousquet, Nicolas Chuet, Quentin Falgas-Ravry, Victor Jacques, Amaury Morelle, Laure |
| contents | In this short note, we prove that every twin-free graph on $n$ vertices contains a locating-dominating set of size at most $\lceil\frac{5}{8}n\rceil$. This improves the earlier bound of $\lfloor\frac{2}{3}n\rfloor$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_18162 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A note on locating-dominating sets in twin-free graphs Bousquet, Nicolas Chuet, Quentin Falgas-Ravry, Victor Jacques, Amaury Morelle, Laure Combinatorics 05C69 G.2.2; F.2.2 In this short note, we prove that every twin-free graph on $n$ vertices contains a locating-dominating set of size at most $\lceil\frac{5}{8}n\rceil$. This improves the earlier bound of $\lfloor\frac{2}{3}n\rfloor$ 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. |
| title | A note on locating-dominating sets in twin-free graphs |
| topic | Combinatorics 05C69 G.2.2; F.2.2 |
| url | https://arxiv.org/abs/2405.18162 |