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Mathematical Notes

, Volume 105, Issue 1–2, pp 16–27 | Cite as

On Lower Bounds for the Chromatic Number of Spheres

  • O. A. KostinaEmail author
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Abstract

Estimates of the chromatic numbers of spheres are studied. The optimality of the choice of the parameters of the linear-algebraic method used to obtain these estimates is investigated. For the case of (0, 1)-vectors, it is shown that the parameters chosen in previous results yield the best estimate. For the case of (−1, 0, 1)-vectors, the optimal values of the parameters are obtained; this leads to a significant refinement of the estimates of the chromatic numbers of spheres obtained earlier.

Keywords

chromatic number of spheres linear-algebraic method Frankl–Wilson theorem Nelson–Hadwiger problem distance graphs 

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Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Moscow Institute of Physics and Technology (State University)Dolgoprudnyi, Moscow OblastRussia

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