RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
 General information Latest issue Archive Impact factor Subscription Guidelines for authors License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Mat. Zametki: Year: Volume: Issue: Page: Find

 Mat. Zametki, 2019, Volume 105, Issue 1, Pages 18–31 (Mi mz11633)

On Lower Bounds for the Chromatic Number of Spheres

O. A. Kostina

Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow region

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.

DOI: https://doi.org/10.4213/mzm11633

Full text: PDF file (518 kB)
First page: PDF file
References: PDF file   HTML file

Document Type: Article
UDC: 517.174.7
Revised: 01.07.2018

Citation: O. A. Kostina, “On Lower Bounds for the Chromatic Number of Spheres”, Mat. Zametki, 105:1 (2019), 18–31

Citation in format AMSBIB
\Bibitem{Kos19} \by O.~A.~Kostina \paper On Lower Bounds for the Chromatic Number of Spheres \jour Mat. Zametki \yr 2019 \vol 105 \issue 1 \pages 18--31 \mathnet{http://mi.mathnet.ru/mz11633} \crossref{https://doi.org/10.4213/mzm11633} \elib{http://elibrary.ru/item.asp?id=36603820}