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Mat. Zametki, 2019, Volume 105, Issue 1, Pages 18–31 (Mi mz11633)  

On Lower Bounds for the Chromatic Number of Spheres

O. A. Kostina

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

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.

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

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English version:
Mathematical Notes, 2019, 105:1, 16–27

Bibliographic databases:

Document Type: Article
UDC: 517.174.7
Received: 28.03.2017
Revised: 01.07.2018

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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