On the chromatic numbers of 3-dimensional slices
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866916110548336640 |
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| author | Cherkashin, D. D. Kanel-Belov, A. J. Strukov, G. A. Voronov, V. A. |
| author_facet | Cherkashin, D. D. Kanel-Belov, A. J. Strukov, G. A. Voronov, V. A. |
| contents | We prove that for an arbitrary $\varepsilon > 0$ holds \[ χ(\mathbb{R}^3 \times [0,\varepsilon]^6) \geq 10, \] where $χ(M)$ stands for the chromatic number of an (infinite) graph with the vertex set $M$ and the edge set consists of pairs of monochromatic points at the distance 1 apart. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_02230 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On the chromatic numbers of 3-dimensional slices Cherkashin, D. D. Kanel-Belov, A. J. Strukov, G. A. Voronov, V. A. Combinatorics Metric Geometry We prove that for an arbitrary $\varepsilon > 0$ holds \[ χ(\mathbb{R}^3 \times [0,\varepsilon]^6) \geq 10, \] where $χ(M)$ stands for the chromatic number of an (infinite) graph with the vertex set $M$ and the edge set consists of pairs of monochromatic points at the distance 1 apart. |
| title | On the chromatic numbers of 3-dimensional slices |
| topic | Combinatorics Metric Geometry |
| url | https://arxiv.org/abs/2208.02230 |