On Dirac and Motzkin problem in discrete geometry
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866929692597026816 |
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| author | Florek, Jan |
| author_facet | Florek, Jan |
| contents | Dirac and Motzkin conjectured that any set X of $n$ non-collinear points in the plane has an element incident with at least $\lceil \frac{n}{2} \rceil$ lines spanned by X. In this paper we prove that any set X of $n$ non-collinear points in the plane, distributed on three lines passing through a common point, has an element incident with at least $\lceil \frac{n}{2} \rceil$ lines spanned by X. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_18406 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Dirac and Motzkin problem in discrete geometry Florek, Jan Combinatorics 05B25, 51M16 Dirac and Motzkin conjectured that any set X of $n$ non-collinear points in the plane has an element incident with at least $\lceil \frac{n}{2} \rceil$ lines spanned by X. In this paper we prove that any set X of $n$ non-collinear points in the plane, distributed on three lines passing through a common point, has an element incident with at least $\lceil \frac{n}{2} \rceil$ lines spanned by X. |
| title | On Dirac and Motzkin problem in discrete geometry |
| topic | Combinatorics 05B25, 51M16 |
| url | https://arxiv.org/abs/2501.18406 |