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On the chromatic numbers of small-dimensional Euclidean spaces. / Cherkashin, Danila; Kulikov, Anatoly; Raigorodskii, Andrei.

In: Discrete Applied Mathematics, Vol. 243, 10.07.2018, p. 125-131.

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

Harvard

Cherkashin, D, Kulikov, A & Raigorodskii, A 2018, 'On the chromatic numbers of small-dimensional Euclidean spaces', Discrete Applied Mathematics, vol. 243, pp. 125-131. https://doi.org/10.1016/j.dam.2018.02.005

APA

Cherkashin, D., Kulikov, A., & Raigorodskii, A. (2018). On the chromatic numbers of small-dimensional Euclidean spaces. Discrete Applied Mathematics, 243, 125-131. https://doi.org/10.1016/j.dam.2018.02.005

Vancouver

Cherkashin D, Kulikov A, Raigorodskii A. On the chromatic numbers of small-dimensional Euclidean spaces. Discrete Applied Mathematics. 2018 Jul 10;243:125-131. https://doi.org/10.1016/j.dam.2018.02.005

Author

Cherkashin, Danila ; Kulikov, Anatoly ; Raigorodskii, Andrei. / On the chromatic numbers of small-dimensional Euclidean spaces. In: Discrete Applied Mathematics. 2018 ; Vol. 243. pp. 125-131.

BibTeX

@article{1da860f3bc134d23bc4830021e30e365,
title = "On the chromatic numbers of small-dimensional Euclidean spaces",
abstract = "This paper is devoted to the study of the graph sequence Gn=(Vn,En), where Vn is the set of all vectors v∈Rn with coordinates in {−1,0,1} such that |v|=3 and En consists of all pairs of vertices with scalar product 1. We find the exact value of the independence number of Gn. As a corollary we get new lower bounds on χ(Rn) and χ(Qn) for small values of n.",
keywords = "Chromatic number, Distance graphs, Independence number, R-N, SETS",
author = "Danila Cherkashin and Anatoly Kulikov and Andrei Raigorodskii",
year = "2018",
month = jul,
day = "10",
doi = "10.1016/j.dam.2018.02.005",
language = "English",
volume = "243",
pages = "125--131",
journal = "Discrete Applied Mathematics",
issn = "0166-218X",
publisher = "Elsevier",

}

RIS

TY - JOUR

T1 - On the chromatic numbers of small-dimensional Euclidean spaces

AU - Cherkashin, Danila

AU - Kulikov, Anatoly

AU - Raigorodskii, Andrei

PY - 2018/7/10

Y1 - 2018/7/10

N2 - This paper is devoted to the study of the graph sequence Gn=(Vn,En), where Vn is the set of all vectors v∈Rn with coordinates in {−1,0,1} such that |v|=3 and En consists of all pairs of vertices with scalar product 1. We find the exact value of the independence number of Gn. As a corollary we get new lower bounds on χ(Rn) and χ(Qn) for small values of n.

AB - This paper is devoted to the study of the graph sequence Gn=(Vn,En), where Vn is the set of all vectors v∈Rn with coordinates in {−1,0,1} such that |v|=3 and En consists of all pairs of vertices with scalar product 1. We find the exact value of the independence number of Gn. As a corollary we get new lower bounds on χ(Rn) and χ(Qn) for small values of n.

KW - Chromatic number

KW - Distance graphs

KW - Independence number

KW - R-N

KW - SETS

UR - http://www.scopus.com/inward/record.url?scp=85044308219&partnerID=8YFLogxK

U2 - 10.1016/j.dam.2018.02.005

DO - 10.1016/j.dam.2018.02.005

M3 - Article

AN - SCOPUS:85044308219

VL - 243

SP - 125

EP - 131

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

SN - 0166-218X

ER -

ID: 36097989