Geodesic
On the chromatic numbers of $3$-dimensional slices
Zapiski Nauchnykh Seminarov POMI, Combinatorics and graph theory. Part XIII, Tome 518 (2022), pp. 94-113 
V. A. Voronov; A. Ya. Kanel-Belov; G. A. Strukov; D. D. Cherkashin. On the chromatic numbers of $3$-dimensional slices. Zapiski Nauchnykh Seminarov POMI, Combinatorics and graph theory. Part XIII, Tome 518 (2022), pp. 94-113. http://geodesic.mathdoc.fr/item/ZNSL_2022_518_a1/
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

We prove that for an arbitrary $\varepsilon > 0$ holds $$ \chi (\mathbb{R}^3 \times [0,\varepsilon]^6) \geq 10, $$ where $\chi(M)$ stands for the chromatic number of an (infinite) graph with the vertex set $M$ and the edge set consists of pairs of points at the distance $1$ apart.

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