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Chebyshevskii Sb., 2018, Volume 19, Issue 3, Pages 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

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


DOI: https://doi.org/10.22405/2226-8383-2018-19-3-270-281

Full text: PDF file (650 kB)
References: PDF file   HTML file

UDC: 514.174.5
Received: 29.07.2018
Accepted:15.10.2018

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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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Yu. A. Demidovich, M. E. Zhukovskii, “Chromatic Numbers of Distance Graphs without Short Odd Cycles in Rational Spaces”, Math. Notes, 109:5 (2021), 727–734  mathnet  crossref  crossref  isi
    2. A. V. Berdnikov, A. M. Raigorodskii, “Otsenki chisel Borsuka po distantsionnym grafam spetsialnogo vida”, Probl. peredachi inform., 57:2 (2021), 44–50  mathnet  crossref
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