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Zapiski Nauchnykh Seminarov POMI, 2022, Volume 518, Pages 94–113 (Mi znsl7293)  
On the chromatic numbers of $3$-dimensional slices

V. A. Voronovab, A. Ya. Kanel-Belovb, G. A. Strukovc, D. D. Cherkashind

a Caucasus Mathematical Center, Adyghe State University, Maikop
b Moscow Institute of Physics and Technology (National Research University), Dolgoprudny, Moscow Region
c St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences
d Institute of Mathematics and Informatics, Bulgarian Academy of Sciences
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Abstract: 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.
Key words and phrases: distance graphs, chromatic number of space.
Funding agency Grant number
Russian Science Foundation 22-11-00177
Received: 01.12.2022
Document Type: Article
UDC: 514.17, 519.174, 515.124.3
Language: Russian
Citation: V. A. Voronov, A. Ya. Kanel-Belov, G. A. Strukov, D. D. Cherkashin, “On the chromatic numbers of $3$-dimensional slices”, Combinatorics and graph theory. Part XIII, Zap. Nauchn. Sem. POMI, 518, POMI, St. Petersburg, 2022, 94–113
Citation in format AMSBIB
\Bibitem{VorKanStr22}
\by V.~A.~Voronov, A.~Ya.~Kanel-Belov, G.~A.~Strukov, D.~D.~Cherkashin
\paper On the chromatic numbers of $3$-dimensional slices
\inbook Combinatorics and graph theory. Part~XIII
\serial Zap. Nauchn. Sem. POMI
\yr 2022
\vol 518
\pages 94--113
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl7293}
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