Three-chromatic geometric hypergraphs
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866908773516312576 |
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| author | Damásdi, Gábor Pálvölgyi, Dömötör |
| author_facet | Damásdi, Gábor Pálvölgyi, Dömötör |
| contents | We prove that for any planar convex body C there is a positive integer m with the property that any finite point set P in the plane can be three-colored such that there is no translate of C containing at least m points of P, all of the same color. As a part of the proof, we show a strengthening of the Erdős-Sands-Sauer-Woodrow conjecture. Surprisingly, the proof also relies on the two dimensional case of the Illumination conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2112_01820 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Three-chromatic geometric hypergraphs Damásdi, Gábor Pálvölgyi, Dömötör Combinatorics Discrete Mathematics We prove that for any planar convex body C there is a positive integer m with the property that any finite point set P in the plane can be three-colored such that there is no translate of C containing at least m points of P, all of the same color. As a part of the proof, we show a strengthening of the Erdős-Sands-Sauer-Woodrow conjecture. Surprisingly, the proof also relies on the two dimensional case of the Illumination conjecture. |
| title | Three-chromatic geometric hypergraphs |
| topic | Combinatorics Discrete Mathematics |
| url | https://arxiv.org/abs/2112.01820 |