On Two-Distance $(0,1)$-Counterexamples to Borsuk's Conjecture in $l_p$ Metrics

A. M. Raigorodskii^abcd, K. A. Smolenskii<sup>a

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

Abstract: Various estimates of the Borsuk number are discussed. A method for constructing two-distance counterexamples to Borsuk's conjecture by using $(0,1)$-vectors in spaces with $l_p$ metrics is considered.

Keywords: Borsuk's conjecture, Borsuk number, independence number, graph of diameters, forbidden distance.

UDC: 519.1

Received: 04.09.2024

DOI: 10.4213/mzm14494

 English version: Mathematical Notes, 2025, 118:1, 158–164

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