Improved lower bound towards Chen-Chvátal conjecture
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866916511435718656 |
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| author | Huang, Congkai |
| author_facet | Huang, Congkai |
| contents | We prove that in every metric space where no line contains all the points, there are at least $Ω(n^{2/3})$ lines. This improves the previous $Ω(\sqrt{n})$ lower bound on the number of lines in general metric space, and also improves the previous $Ω(n^{4/7})$ lower bound on the number of lines in metric spaces generated by connected graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_15058 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Improved lower bound towards Chen-Chvátal conjecture Huang, Congkai Combinatorics We prove that in every metric space where no line contains all the points, there are at least $Ω(n^{2/3})$ lines. This improves the previous $Ω(\sqrt{n})$ lower bound on the number of lines in general metric space, and also improves the previous $Ω(n^{4/7})$ lower bound on the number of lines in metric spaces generated by connected graphs. |
| title | Improved lower bound towards Chen-Chvátal conjecture |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2310.15058 |