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Mathematical Notes

, Volume 105, Issue 1–2, pp 180–203 | Cite as

A Remark on Lower Bounds for the Chromatic Numbers of Spaces of Small Dimension with Metrics 1 and 2

  • L. I. BogolyubskyEmail author
  • A. M. RaigorodskiiEmail author
Article
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Abstract

A particular class of estimates related to the Nelson–Erdős–Hadwiger problem is studied. For two types of spaces, Euclidean and spaces with metric 1, certain series of distance graphs of small dimensions are considered. Independence numbers of such graphs are estimated by using the linear-algebraic method and combinatorial observations. This makes it possible to obtain certain lower bounds for the chromatic numbers of the spaces mentioned above and, for each case, specify a series of graphs leading to the strongest results.

Keywords

chromatic number chromatic number of a metric space independence number linear-algebraic method distance graph 

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Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Lomonosov Moscow State UniversityMoscowRussia
  2. 2.Moscow Institute of Physics and Technology (State University)Dolgoprudnyi, Moscow OblastRussia
  3. 3.Adygeya State UniversityMaikopRussia
  4. 4.Buryat State UniversityUlan-UdeRussia

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