O. A. Kostina, “On Lower Bounds for the Chromatic Number of Spheres”, Mat. Zametki, 105:1 (2019), 18–31; Math. Notes, 105:1 (2019), 16

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Matematicheskie Zametki, 2019, Volume 105, Issue 1, Pages 18–31
DOI: https://doi.org/10.4213/mzm11633 (Mi mzm11633)

This article is cited in 14 scientific papers (total in 14 papers)

On Lower Bounds for the Chromatic Number of Spheres

O. A. Kostina

Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow region

Full-text PDF (518 kB) Citations (14)

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DOI: https://doi.org/10.4213/mzm11633

Abstract: Estimates of the chromatic numbers of spheres are studied. The optimality of the choice of the parameters of the linear-algebraic method used to obtain these estimates is investigated. For the case of $(0,1)$-vectors, it is shown that the parameters chosen in previous results yield the best estimate. For the case of $(-1,0,1)$-vectors, the optimal values of the parameters are obtained; this leads to a significant refinement of the estimates of the chromatic numbers of spheres obtained earlier.

Keywords: chromatic number of spheres, linear-algebraic method, Frankl–Wilson theorem, Nelson–Hadwiger problem, distance graphs.

Received: 28.03.2017
Revised: 01.07.2018

English version:
Mathematical Notes, 2019, Volume 105, Issue 1, Pages 16–27
DOI: https://doi.org/10.1134/S0001434619010036

Bibliographic databases:

Document Type: Article

UDC: 517.174.7

Language: Russian

Citation: O. A. Kostina, “On Lower Bounds for the Chromatic Number of Spheres”, Mat. Zametki, 105:1 (2019), 18–31; Math. Notes, 105:1 (2019), 16–27

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https://doi.org/10.4213/mzm11633

https://www.mathnet.ru/eng/mzm/v105/i1/p18

This publication is cited in the following 14 articles:

Danila Cherkashin, Vsevolod Voronov, “On the Chromatic Number of 2-Dimensional Spheres”, Discrete Comput Geom, 71:2 (2024), 467
M.M. Ipatov, M.M. Koshelev, A.M. Raigorodskii, “Modularity of some distance graphs”, European Journal of Combinatorics, 117 (2024), 103833
V.A. Voronov, A.M. Neopryatnaya, E.A. Dergachev, “Constructing 5-chromatic unit distance graphs embedded in the Euclidean plane and two-dimensional spheres”, Discrete Mathematics, 345:12 (2022), 113106
Mikhail M. Koshelev, “Lower bounds on the clique-chromatic numbers of some distance graphs”, Moscow J. Comb. Number Th., 10:2 (2021), 141
Mikhail Koshelev, “New lower bound on the modularity of Johnson graphs”, Moscow J. Comb. Number Th., 10:1 (2021), 77
Mikhail Ipatov, “Exact modularity of line graphs of complete graphs”, Moscow J. Comb. Number Th., 10:1 (2021), 61
Nikita Derevyanko, Mikhail Koshelev, Andrei Raigorodskii, Trends in Mathematics, 14, Extended Abstracts EuroComb 2021, 2021, 221
M. M. Ipatov, M. Koshelev, A. M. Raigorodskii, “Modularity of some distance graphs”, Dokl. Math., 101:1 (2020), 60–61
A. M. Raigorodskii, M. Koshelev, “New bounds for the clique-chromatic numbers of Johnson graphs”, Dokl. Math., 101:1 (2020), 66–67
A. M. Raigorodskii, M. M. Koshelev, “New bounds on clique-chromatic numbers of johnson graphs”, Discret Appl. Math., 283 (2020), 724–729
Yu. A. Demidovich, “Distance Graphs with Large Chromatic Number and without Cliques of Given Size in the Rational Space”, Math. Notes, 106:1 (2019), 38–51
A. A. Sagdeev, “On a Frankl–Wilson Theorem”, Problems Inform. Transmission, 55:4 (2019), 376–395
Raigorodskii A.M. Shishunov E.D., “On the Independence Numbers of Distance Graphs With Vertices in (-1,0,1)(N)”, Dokl. Math., 100:2 (2019), 476–477
A. A. Sokolov, A. M. Raigorodskii, “O ratsionalnykh analogakh problem Nelsona–Khadvigera i Borsuka”, Chebyshevskii sb., 19:3 (2018), 270–281

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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