This article is cited in 3 papers

MATHEMATICS

Covering planar sets

A. D. Tolmachev, D. S. Protasov

Moscow Institute of Physics and Technology (National Research University), Moscow, Russia

Abstract: Methods for improving upper and lower bounds for various coverings of planar sets are proposed. New bounds for various numbers of partition constituents are presented, and suggestions for the generalization of the presented methods are offered.

Keywords: Borsuk problem, diameter of a set, coverings of planar sets, universal covering systems, chromatic number.

UDC: 517

Presented: V. V. Kozlov
Received: 22.04.2021
Revised: 22.04.2021
Accepted: 02.05.2021

DOI: 10.31857/S2686954321040147

 English version: Doklady Mathematics, 2021, 104:1, 196–199

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