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arXiv · 1512.06444

On the cromatic number of infinitesimal plane layer

A. J. Kanel-Belov·V. Voronov·D. Cherkashin
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Abstract

We consider natural generalization of plane chromatic number problem. We consider chromatic numbers $χ$ of spaces $\mathbb{R}^n \times [0,\varepsilon]^k$ for arbitrary small $\varepsilon$. We prove that $5 \leqχ(\mathbb{R}^2\times [0,\varepsilon])\leq 7$ and ${6\leq χ(\mathbb{R}^2\times [0,\varepsilon]^2) \leq 7}$. Also we consider natural questions, arising from this considerations.

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A. J. Kanel-Belov, V. Voronov, D. Cherkashin. 2017-10-22. On the cromatic number of infinitesimal plane layer. https://arxiv.org/abs/1512.06444

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