On the chromatic number of an infinitesimal plane layer

A. Ya Kanel-Belov; V. A. Voronov; D. D. Cherkashin

doi:10.1090/spmj/1515

On the chromatic number of an infinitesimal plane layer

A. Ya Kanel-Belov, V. A. Voronov, D. D. Cherkashin

Research output: Contribution to journal › Article › peer-review

Abstract

This paper is devoted to a natural generalization of the problem on the chromatic number of the plane. The chromatic number of the spaces ℝⁿ × [0, ε]^k is considered. It is proved that 5 ≤ χ(ℝ² × [0, ε]) ≤ 7 and 6 ≤ χ(ℝ² × [0, ε]²) ≤ 7 for ε > 0 sufficiently small. Also, some natural questions arising from these considerations are posed.

Original language	English
Pages (from-to)	761-775
Number of pages	15
Journal	St. Petersburg Mathematical Journal
Volume	29
Issue number	5
DOIs	https://doi.org/10.1090/spmj/1515
State	Published - 2018
Externally published	Yes

Keywords

Chromatic number of Euclidean spaces
Chromatic number of the plane

All Science Journal Classification (ASJC) codes

Analysis
Algebra and Number Theory
Applied Mathematics

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10.1090/spmj/1515

Cite this

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abstract = "This paper is devoted to a natural generalization of the problem on the chromatic number of the plane. The chromatic number of the spaces ℝn × [0, ε]k is considered. It is proved that 5 ≤ χ(ℝ2 × [0, ε]) ≤ 7 and 6 ≤ χ(ℝ2 × [0, ε]2) ≤ 7 for ε > 0 sufficiently small. Also, some natural questions arising from these considerations are posed.",

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N2 - This paper is devoted to a natural generalization of the problem on the chromatic number of the plane. The chromatic number of the spaces ℝn × [0, ε]k is considered. It is proved that 5 ≤ χ(ℝ2 × [0, ε]) ≤ 7 and 6 ≤ χ(ℝ2 × [0, ε]2) ≤ 7 for ε > 0 sufficiently small. Also, some natural questions arising from these considerations are posed.

AB - This paper is devoted to a natural generalization of the problem on the chromatic number of the plane. The chromatic number of the spaces ℝn × [0, ε]k is considered. It is proved that 5 ≤ χ(ℝ2 × [0, ε]) ≤ 7 and 6 ≤ χ(ℝ2 × [0, ε]2) ≤ 7 for ε > 0 sufficiently small. Also, some natural questions arising from these considerations are posed.

KW - Chromatic number of Euclidean spaces

KW - Chromatic number of the plane

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M3 - مقالة

SN - 1061-0022

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EP - 775

JO - St. Petersburg Mathematical Journal

JF - St. Petersburg Mathematical Journal

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ER -

On the chromatic number of an infinitesimal plane layer

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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