Email this article Chromatic Number with Several Forbidden Distances in the Space with the ℓq-Metric
- Authors: Berdnikov A.V.1
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Affiliations:
- M. V. Lomonosov Moscow State University
- Issue: Vol 227, No 4 (2017)
- Pages: 395-401
- Section: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/240145
- DOI: https://doi.org/10.1007/s10958-017-3592-0
- ID: 240145
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Abstract
We study the chromatic number \( \overline{\chi}\left(X;\rho; k\right) \) of a metric space X with a metric ρ and k forbidden distances. We obtain an estimate of the form \( \overline{\chi}\left({\mathbb{R}}^n;\rho; k\right)\ge {(Bk)}^{Cn} \) for cases where the metric ρ on the set ℝn is generated by the ℓq-norm.
About the authors
A. V. Berdnikov
M. V. Lomonosov Moscow State University
Author for correspondence.
Email: alexey-berdnikov@yandex.ru
Russian Federation, Moscow
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