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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
Citation in format AMSBIB
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    • This publication is cited in the following 14 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Математические заметки Mathematical Notes
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