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Mat. Zametki, 2019, Volume 105, Issue 2, Pages 187–213 (Mi mz11736)  

This article is cited in 5 scientific papers (total in 5 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

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.

Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/mzm11736

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English version:
Mathematical Notes, 2019, 105:2, 180–203

Bibliographic databases:

UDC: 519.174.7
PACS: -
Received: 05.07.2017
Revised: 01.12.2017

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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\by L.~I.~Bogolubsky, A.~M.~Raigorodskii
\paper A Remark on Lower Bounds for the Chromatic Numbers of Spaces of Small Dimension with Metrics $\ell_1$ and $\ell_2$
\jour Mat. Zametki
\yr 2019
\vol 105
\issue 2
\pages 187--213
\mathnet{http://mi.mathnet.ru/mz11736}
\crossref{https://doi.org/10.4213/mzm11736}
\elib{https://elibrary.ru/item.asp?id=37045105}
\transl
\jour Math. Notes
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\vol 105
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\pages 180--203
\crossref{https://doi.org/10.1134/S000143461901022X}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. A. Sokolov, A. M. Raigorodskii, “O ratsionalnykh analogakh problem Nelsona–Khadvigera i Borsuka”, Chebyshevskii sb., 19:3 (2018), 270–281  mathnet  crossref  elib
    2. R. I. Prosanov, “Counterexamples to Borsuk's Conjecture with Large Girth”, Math. Notes, 105:6 (2019), 874–880  mathnet  crossref  crossref  isi  elib
    3. K. D. Kovalenko, A. M. Raigorodskii, “Systems of Representatives”, Math. Notes, 106:3 (2019), 372–377  mathnet  crossref  crossref  isi  elib
    4. A. A. Sagdeev, “On a Frankl–Wilson Theorem”, Problems Inform. Transmission, 55:4 (2019), 376–395  mathnet  crossref  crossref  isi  elib
    5. Ph. A. Pushnyakov, A. M. Raigorodskii, “Estimate of the Number of Edges in Special Subgraphs of a Distance Graph”, Math. Notes, 107:2 (2020), 322–332  mathnet  crossref  crossref  isi  elib
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