A. M. Raigorodskii, “On dividing sets into parts of smaller diameter”, Dokl. RAN. Math. Inf. Proc. Upr., 2020, Volume 495,Pages <nobr>74–77</nobr>

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Dokl. RAN. Math. Inf. Proc. Upr., 2020 Volume 495, Pages 74–77 (Mi danma138)

This article is cited in 4 papers

MATHEMATICS

On dividing sets into parts of smaller diameter

A. M. Raigorodskii^abcd

^a Moscow Institute of Physics and Technology (National Research University), Dolgoprudny, Moscow Region, Russian Federation
^b Lomonosov Moscow State University, Moscow, Russian Federation
^c Caucasus Mathematical Center, Adyghe State University, Maykop, Russian Federation
^d Buryat State University, Institute for Mathematics and Informatics, Ulan-Ude, Russian Federation

Abstract: An important generalization of Borsuk's classical problem of partitioning sets into parts of smaller diameter is studied. New upper and lower bounds for the Borsuk numbers are found.

Keywords: partition, coloring, point sets in spaces, diameter graph.

UDC: 517

Presented: V. V. Kozlov
Received: 05.07.2020
Revised: 05.07.2020
Accepted: 17.09.2020

DOI: 10.31857/S2686954320060156

English version: Doklady Mathematics, 2020, 102:3, 510–512

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