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Matematicheskie Zametki, 2019, Volume 105, Issue 2, Pages 187–213
DOI: https://doi.org/10.4213/mzm11736 (Mi mzm11736) 		 
This article is cited in 24 scientific papers (total in 24 papers)

A Remark on Lower Bounds for the Chromatic Numbers of Spaces of Small Dimension with Metrics $\ell_1$ and $\ell_2$

L. I. Bogolubskya, A. M. Raigorodskiibacd

a Lomonosov Moscow State University
b Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow region
c Buryat State University, Ulan-Ude
d Caucasus Mathematical Center, Adyghe State University, Maikop
Full-text PDF (717 kB) Citations (24)
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DOI: https://doi.org/10.4213/mzm11736
Abstract: A particular class of estimates related to the Nelson–Erdős–Hadwiger problem is studied. For two types of spaces, Euclidean and spaces with metric $\ell_1$, certain series of distance graphs of small dimensions are considered. Independence numbers of such graphs are estimated by using the linear-algebraic method and combinatorial observations. This makes it possible to obtain certain lower bounds for the chromatic numbers of the spaces mentioned above and, for each case, specify a series of graphs leading to the strongest results.
Keywords: chromatic number, chromatic number of a metric space, independence number, linear-algebraic method, distance graph.
Funding agency Grant number
Russian Foundation for Basic Research 15-01-03530
This work was supported by the Russian Foundation for Basic Research under grant 15-01-03530.
Received: 05.07.2017
Revised: 01.12.2017
English version:
Mathematical Notes, 2019, Volume 105, Issue 2, Pages 180–203
DOI: https://doi.org/10.1134/S000143461901022X
Bibliographic databases:
Document Type: Article
UDC: 519.174.7
PACS: -
Language: Russian
Citation: L. I. Bogolubsky, A. M. Raigorodskii, “A Remark on Lower Bounds for the Chromatic Numbers of Spaces of Small Dimension with Metrics $\ell_1$ and $\ell_2$”, Mat. Zametki, 105:2 (2019), 187–213; Math. Notes, 105:2 (2019), 180–203
Citation in format AMSBIB
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\paper A Remark on Lower Bounds for the Chromatic Numbers of Spaces of Small Dimension with Metrics $\ell_1$ and $\ell_2$
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\pages 187--213
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    • This publication is cited in the following 24 articles:
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