This article is cited in 3 papers

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

A. Sokolov^a, A. M. Raigorodskiy<sup>bcda

a</sup> 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.

UDC: 514.174.5

Received: 29.07.2018
Accepted: 15.10.2018

DOI: 10.22405/2226-8383-2018-19-3-270-281

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