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Chebyshevskii Sbornik, 2018, Volume 19, Issue 3, Pages 270–281
DOI: https://doi.org/10.22405/2226-8383-2018-19-3-270-281 (Mi cheb694) 		 
This article is cited in 2 scientific papers (total in 2 papers)

On rational analogs of Nelson–Hadwiger's and Borsuk's problems

A. Sokolova, A. M. Raigorodskiybcda

a Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
b Moscow Institute of Physics and Technology (State University)
c Buryat State University, Institute for Mathematics and Informatics
d Caucasus Mathematical Center, Adyghe State University
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DOI: https://doi.org/10.22405/2226-8383-2018-19-3-270-281
Abstract: In this paper, we consider affine-rational analogs of Nelson–Hadwiger problem on finding the chromatic number of the rational space and Borsuk's problem on partitioning into parts of smaller diameter. New lower bounds are proved. In particular, bounds on the minimum dimension of a counterexample to Borsuk's conjecture are found.
Keywords: Chromatic number, unit-distance graphs, Borsuk's problem.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation НШ-6760.2018.1
Russian Foundation for Basic Research 18-01-00355_а
Received: 29.07.2018
Accepted: 15.10.2018
Bibliographic databases:
Document Type: Article
UDC: 514.174.5
Language: Russian
Citation: A. Sokolov, A. M. Raigorodskiy, “On rational analogs of Nelson–Hadwiger's and Borsuk's problems”, Chebyshevskii Sb., 19:3 (2018), 270–281
Citation in format AMSBIB
\Bibitem{SokRai18}
\by A.~Sokolov, A.~M.~Raigorodskiy
\paper On rational analogs of Nelson--Hadwiger's and Borsuk's problems
\jour Chebyshevskii Sb.
\yr 2018
\vol 19
\issue 3
\pages 270--281
\mathnet{http://mi.mathnet.ru/cheb694}
\crossref{https://doi.org/10.22405/2226-8383-2018-19-3-270-281}
\elib{https://elibrary.ru/item.asp?id=39454403}
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    References:28
     
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