Progressions in Euclidean Ramsey theory
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912157265821696 |
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| author | Führer, Jakob Tóth, Géza |
| author_facet | Führer, Jakob Tóth, Géza |
| contents | Conlon and Wu showed that there is a red/blue-coloring of $\mathbb{E}^n$ that does not contain $3$ red collinear points separated by unit distance and $m=10^{50}$ blue collinear points separated by unit distance. We prove that the statement holds with $m=1177$. We show similar results with different distances between the points. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_12567 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Progressions in Euclidean Ramsey theory Führer, Jakob Tóth, Géza Combinatorics 05C55, 05D10, 11B25, 52C99 Conlon and Wu showed that there is a red/blue-coloring of $\mathbb{E}^n$ that does not contain $3$ red collinear points separated by unit distance and $m=10^{50}$ blue collinear points separated by unit distance. We prove that the statement holds with $m=1177$. We show similar results with different distances between the points. |
| title | Progressions in Euclidean Ramsey theory |
| topic | Combinatorics 05C55, 05D10, 11B25, 52C99 |
| url | https://arxiv.org/abs/2402.12567 |