E. I. Ponomarenko, A. M. Raigorodskii, “New Lower Bound for the Chromatic Number of a Rational Space with One and Two Forbidden Distances”, Mat. Zametki, 97:2 (2015), 255–261; Math. Notes, 97:2 (2015), 249

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Matematicheskie Zametki, 2015, Volume 97, Issue 2, Pages 255–261
DOI: https://doi.org/10.4213/mzm10383 (Mi mzm10383)

This article is cited in 11 scientific papers (total in 11 papers)

New Lower Bound for the Chromatic Number of a Rational Space with One and Two Forbidden Distances

E. I. Ponomarenko^a, A. M. Raigorodskii^ba

^a Moscow Institute of Physics and Technology (State University), Dolgoprudnyi, Moskovskaya obl.
^b M. V. Lomonosov Moscow State University

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DOI: https://doi.org/10.4213/mzm10383

Abstract: A new lower bound for the chromatic number

$\chi({\mathbb Q}^n)$ of the space

${\mathbb Q}^n$ is obtained.

Keywords: chromatic number, rational space with forbidden distances, Nelson–Hadwiger problem, independence number of a graph, Stirling's formula.

Funding agency	Grant number
Russian Foundation for Basic Research	12-01-00683
Ministry of Education and Science of the Russian Federation	МД-6277.2013.1 НШ-2964.2014.1
This work was supported by the Russian Foundation for Basic Research (grant no. 12-01-00683), Grant of the President of the Russian Federation no. MD-6277.2013.1, and by the program “Leading Scientific Schools” (grant no. NSh-2964.2014.1).

Received: 07.08.2013
Revised: 03.04.2014

English version:
Mathematical Notes, 2015, Volume 97, Issue 2, Pages 249–254
DOI: https://doi.org/10.1134/S0001434615010265

Bibliographic databases:

Document Type: Article

UDC: 519.17

Language: Russian

Citation: E. I. Ponomarenko, A. M. Raigorodskii, “New Lower Bound for the Chromatic Number of a Rational Space with One and Two Forbidden Distances”, Mat. Zametki, 97:2 (2015), 255–261; Math. Notes, 97:2 (2015), 249–254

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/mzm10383

https://doi.org/10.4213/mzm10383

https://www.mathnet.ru/eng/mzm/v97/i2/p255

This publication is cited in the following 11 articles:

Yu. A. Demidovich, M. E. Zhukovskii, “Chromatic Numbers of Distance Graphs without Short Odd Cycles in Rational Spaces”, Math. Notes, 109:5 (2021), 727–734
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 $\ell_2$ ”, Math. Notes, 105:2 (2019), 180–203
A. V. Bobu, A. E. Kupriyanov, “Refinement of Lower Bounds of the Chromatic Number of a Space with Forbidden One-Color Triangles”, Math. Notes, 105:3 (2019), 329–341
Yu. A. Demidovich, “Distance Graphs with Large Chromatic Number and without Cliques of Given Size in the Rational Space”, Math. Notes, 106:1 (2019), 38–51
A. Sokolov, “On the Chromatic Numbers of Rational Spaces”, Math. Notes, 103:1-2 (2018), 111–117
A. M. Raigorodskii, A. A. Sagdeev, “On a bound in extremal combinatorics”, Dokl. Math., 97:1 (2018), 47–48
A. A. Sokolov, A. M. Raigorodskii, “O ratsionalnykh analogakh problem Nelsona–Khadvigera i Borsuka”, Chebyshevskii sb., 19:3 (2018), 270–281
Roman Prosanov, “Chromatic numbers of spheres”, Discrete Mathematics, 341:11 (2018), 3123
Yu. A. Demidovich, “Lower Bound for the Chromatic Number of a Rational Space with Metric $l_u$ and with One Forbidden Distance”, Math. Notes, 102:4 (2017), 492–507
A. Ya. Kanel-Belov, V. A. Voronov, D. D. Cherkashin, “On the chromatic number of infinitesimal plane layer”, St. Petersburg Math. J., 29:5 (2018), 761–775
L. E. Shabanov, A. M. Raigorodskii, “Turan-type bounds for distance graphs”, Dokl. Math., 96:1 (2017), 351–353

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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