Lines on digraphs of low diameter
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866910674093867008 |
|---|---|
| author | Araujo-Pardo, Gabriela Matamala, Martín Peña, Juan P. Zamora, José |
| author_facet | Araujo-Pardo, Gabriela Matamala, Martín Peña, Juan P. Zamora, José |
| contents | A set of n non-collinear points in the Euclidean plane defines at least n different lines. Chen and Chvtal in 2008 conjectured that the same results is true in metric spaces for an adequate definition of line. More recently, it was conjectured in 2018 by Aboulker et al. that any large enough bridgeless graph on n vertices defines a metric space that has at least n lines. We study the natural extension of Aboulker et al.'s conjecture into the context of quasi-metric spaces defined by digraphs of low diameter. We prove that it is valid for quasi-metric spaces defined by bipartite digraphs of diameter at most three, oriented graphs of diameter two and, digraphs of diameter three and directed girth four. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_21433 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Lines on digraphs of low diameter Araujo-Pardo, Gabriela Matamala, Martín Peña, Juan P. Zamora, José Combinatorics 05c20, 05c12, 52c99 A set of n non-collinear points in the Euclidean plane defines at least n different lines. Chen and Chvtal in 2008 conjectured that the same results is true in metric spaces for an adequate definition of line. More recently, it was conjectured in 2018 by Aboulker et al. that any large enough bridgeless graph on n vertices defines a metric space that has at least n lines. We study the natural extension of Aboulker et al.'s conjecture into the context of quasi-metric spaces defined by digraphs of low diameter. We prove that it is valid for quasi-metric spaces defined by bipartite digraphs of diameter at most three, oriented graphs of diameter two and, digraphs of diameter three and directed girth four. |
| title | Lines on digraphs of low diameter |
| topic | Combinatorics 05c20, 05c12, 52c99 |
| url | https://arxiv.org/abs/2410.21433 |