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On the chromatic number of an infinitesimal plane layer. / Kanel-Belov, A. Ya; Voronov, V. A.; Cherkashin, D. D.

In: St. Petersburg Mathematical Journal, Vol. 29, No. 5, 01.01.2018, p. 761-775.

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

Harvard

Kanel-Belov, AY, Voronov, VA & Cherkashin, DD 2018, 'On the chromatic number of an infinitesimal plane layer', St. Petersburg Mathematical Journal, vol. 29, no. 5, pp. 761-775. https://doi.org/10.1090/spmj/1515

APA

Kanel-Belov, A. Y., Voronov, V. A., & Cherkashin, D. D. (2018). On the chromatic number of an infinitesimal plane layer. St. Petersburg Mathematical Journal, 29(5), 761-775. https://doi.org/10.1090/spmj/1515

Vancouver

Kanel-Belov AY, Voronov VA, Cherkashin DD. On the chromatic number of an infinitesimal plane layer. St. Petersburg Mathematical Journal. 2018 Jan 1;29(5):761-775. https://doi.org/10.1090/spmj/1515

Author

Kanel-Belov, A. Ya ; Voronov, V. A. ; Cherkashin, D. D. / On the chromatic number of an infinitesimal plane layer. In: St. Petersburg Mathematical Journal. 2018 ; Vol. 29, No. 5. pp. 761-775.

BibTeX

@article{af6746eb43c04a3f9dfcd27796c33dd6,
title = "On the chromatic number of an infinitesimal plane layer",
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.",
keywords = "Chromatic number of Euclidean spaces, Chromatic number of the plane, SPACE, chromatic number of Euclidean spaces, DISTANCES, SUBSETS, REALIZATION",
author = "Kanel-Belov, {A. Ya} and Voronov, {V. A.} and Cherkashin, {D. D.}",
year = "2018",
month = jan,
day = "1",
doi = "10.1090/spmj/1515",
language = "English",
volume = "29",
pages = "761--775",
journal = "St. Petersburg Mathematical Journal",
issn = "1061-0022",
publisher = "American Mathematical Society",
number = "5",

}

RIS

TY - JOUR

T1 - On the chromatic number of an infinitesimal plane layer

AU - Kanel-Belov, A. Ya

AU - Voronov, V. A.

AU - Cherkashin, D. D.

PY - 2018/1/1

Y1 - 2018/1/1

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

KW - SPACE

KW - chromatic number of Euclidean spaces

KW - DISTANCES

KW - SUBSETS

KW - REALIZATION

UR - http://www.scopus.com/inward/record.url?scp=85051003158&partnerID=8YFLogxK

U2 - 10.1090/spmj/1515

DO - 10.1090/spmj/1515

M3 - Article

AN - SCOPUS:85051003158

VL - 29

SP - 761

EP - 775

JO - St. Petersburg Mathematical Journal

JF - St. Petersburg Mathematical Journal

SN - 1061-0022

IS - 5

ER -

ID: 36098250