On the chromatic numbers of low-dimensional spaces

Abstract

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.

This is a preview of subscription content, log in to check access.

References

  1. 1.

    A. M. Raigorodskii, Russ. Math. Surv. 56 (1), 103–139 (2001).

    Article  Google Scholar 

  2. 2.

    O. Nechushtan, Discrete Math. 256, 499–507 (2002).

    MathSciNet  Article  Google Scholar 

  3. 3.

    K. Cantwell, J. Combin. Theory A 73 (2), 273–285 (1996).

    MathSciNet  Article  Google Scholar 

  4. 4.

    L. L. Ivanov, Russ. Math. Surv. 61 (5), 984–986 (2006).

    Article  Google Scholar 

  5. 5.

    A. B. Kupavskii, Sb. Math. 202 (6), 859–886 (2011).

    MathSciNet  Article  Google Scholar 

  6. 6.

    J. Cibulka, Geombinatorics 18 (2), 53–66 (2008).

    MathSciNet  Google Scholar 

  7. 7.

    D. G. Larman and C. A. Rogers, Mathematika 19, 1–24 (1972).

    MathSciNet  Article  Google Scholar 

  8. 8.

    A. B. Kupavskii and A. M. Raigorodskii, J. Math. Sci. (New York) 163 (6), 720–731 (2009).

    MathSciNet  Article  Google Scholar 

  9. 9.

    A. Kupavskiy, Discrete Math. 311 (6), 437–440 (2011).

    MathSciNet  Article  Google Scholar 

  10. 10.

    M. Kahle and B. Taha, http://arxiv.org/pdf/1409.1278v1.pdf.

  11. 11.

    G. Exoo and D. Ismailescu, http://arxiv.org/pdf/1408.2002v1.pdf.

  12. 12.

    Z. Nagy, Mat. Lapok 23 (301–302), 26 (1972).

    Google Scholar 

  13. 13.

    L. I. Bogolyubsky, A. S. Gusev, M. M. Pyaderkin, and A. M. Raigorodskii, Sb. Math. 206 (10), 1340–1374 (2015).

    MathSciNet  Article  Google Scholar 

  14. 14.

    A. S. Gusev, Math. Notes 97 (3), 326–332 (2015).

    MathSciNet  Article  Google Scholar 

  15. 15.

    M. M. Pyaderkin, Math. Notes 99 (2), 312–319 (2016).

    MathSciNet  Article  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to A. M. Raigorodskii.

Additional information

Original Russian Text © D.D. Cherkashin, A.M. Raigorodskii, 2017, published in Doklady Akademii Nauk, 2017, Vol. 472, No. 1, pp. 11–12.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Cherkashin, D.D., Raigorodskii, A.M. On the chromatic numbers of low-dimensional spaces. Dokl. Math. 95, 5–6 (2017). https://doi.org/10.1134/S106456241701001X

Download citation