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.
\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}
Linking options:
https://www.mathnet.ru/eng/cheb694
https://www.mathnet.ru/eng/cheb/v19/i3/p270
This publication is cited in the following 2 articles:
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
A. V. Berdnikov, A. M. Raigorodskii, “Bounds on Borsuk numbers in distance graphs of a special type”, Problems Inform. Transmission, 57:2 (2021), 136–142
Citation in format AMSBIB
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