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JOURNALS // Matematicheskii Sbornik // Archive

Mat. Sb., 2008 Volume 199, Number 4, Pages 107–142 (Mi sm3834)

This article is cited in 24 papers

Chromatic numbers of real and rational spaces with real or rational forbidden distances

A. M. Raigorodskii, I. M. Shitova

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: Several important aspects of the Nelson-Erdős-Hadwiger classical problem of combinatorial geometry are considered. In particular, new lower bounds are obtained for the chromatic numbers of the spaces $\mathbb{R}^n$ and $\mathbb{Q}^n$ with two, three or four forbidden distances.
Bibliography: 28 titles.

UDC: 519.174

MSC: Primary 52C10; Secondary 05C15, 51M99

Received: 26.01.2007

DOI: 10.4213/sm3834


 English version:
Sbornik: Mathematics, 2008, 199:4, 579–612

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© Steklov Math. Inst. of RAS, 2026