General penny graphs are at most 43/18-dense
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866908379265368064 |
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| author | Sagdeev, Arsenii |
| author_facet | Sagdeev, Arsenii |
| contents | We prove that among $n$ points in the plane in general position, the shortest distance occurs at most $43n/18$ times, improving upon the upper bound of $17n/7$ obtained by Tóth in 1997. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_09131 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | General penny graphs are at most 43/18-dense Sagdeev, Arsenii Combinatorics Computational Geometry Metric Geometry 52C10, 52C15, 05C10 We prove that among $n$ points in the plane in general position, the shortest distance occurs at most $43n/18$ times, improving upon the upper bound of $17n/7$ obtained by Tóth in 1997. |
| title | General penny graphs are at most 43/18-dense |
| topic | Combinatorics Computational Geometry Metric Geometry 52C10, 52C15, 05C10 |
| url | https://arxiv.org/abs/2402.09131 |