On the Chromatic Numbers of Low-Dimensional Spaces

被引：15

作者：

Cherkashin, D. D. ^{[1
,2
,3
]}

Raigorodskii, A. M. ^{[2
,4
,5
]}

机构：

[1] St Petersburg State Univ, St Petersburg, Russia

[2] State Univ, Moscow Inst Phys & Technol, Dolgoprudnyi 141700, Moscow Oblast, Russia

[3] Univ Geneva, Geneva, Switzerland

[4] Moscow MV Lomonosov State Univ, Fac Mech & Math, Moscow 119992, Russia

[5] Buryat State Univ, Inst Math & Informat, Ulan Ude 670000, Buryat Republic, Russia

来源：

DOKLADY MATHEMATICS | 2017年 / 95卷 / 01期

基金：

俄罗斯科学基金会;

关键词：

INDEPENDENCE NUMBERS; RANDOM SUBGRAPHS; DISTANCE GRAPH; R-N;

D O I：

10.1134/S106456241701001X

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

New lower bounds are found for the minimum number of colors needed to color all points of a Euclidean space in such a way that any two points at a distance of 1 have different colors.

引用

页码：5 / 6

页数：2

共 13 条

[1] On the chromatic number of ℝ9 [J].

Kupavskii A.B. ;

Raigorodskii A.M. .

Journal of Mathematical Sciences, 2009, 163 (6) :720-731

[2]

[Anonymous], GEOMBINATORICS

[3] Independence numbers and chromatic numbers of the random subgraphs of some distance graphs [J].

Bogolubsky, L. I. ;

Gusev, A. S. ;

Pyaderkin, M. M. ;

Raigorodskii, A. M. .

SBORNIK MATHEMATICS, 2015, 206 (10) :1340-1374

[4] Finite Euclidean Ramsey theory [J].

Cantwell, K .

JOURNAL OF COMBINATORIAL THEORY SERIES A, 1996, 73 (02) :273-285

[5]

Gusev AS, 2015, MATH NOTES+, V97, P326, DOI [10.4213/mzm10550, 10.1134/S0001434615030037]

[6] An estimate for the chromatic number of the space R4 [J].

Ivanov, L. L. .

RUSSIAN MATHEMATICAL SURVEYS, 2006, 61 (05) :984-986

[7] On the colouring of spheres embedded in Rn [J].

Kupavskii, A. B. .

SBORNIK MATHEMATICS, 2011, 202 (5-6) :859-886

[8] On the chromatic number of Rn with an arbitrary norm [J].

Kupavskiy, Andrey .

DISCRETE MATHEMATICS, 2011, 311 (06) :437-440

[9] REALIZATION OF DISTANCES WITHIN SETS IN EUCLIDEAN SPACE [J].

LARMAN, DG ;

ROGERS, CA .

MATHEMATIKA, 1972, 19 (37) :1-&

[10]

Nagy Z., 1972, MAT LAPOK, V23, P26

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