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Matematicheskie Zametki, 2007, Volume 81, Issue 5, Pages 733–743
DOI: https://doi.org/10.4213/mzm3717 (Mi mzm3717) 		 
This article is cited in 17 scientific papers (total in 17 papers)

Colorings of the Space $\mathbb R^n$ with Several Forbidden Distances

N. G. Moshchevitin, A. M. Raigorodskii

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Full-text PDF (561 kB) Citations (17)
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DOI: https://doi.org/10.4213/mzm3717
Abstract: The paper is concerned with the classical problem concerning the chromatic number of a metric space, i.e., the minimal number of colors required to color all points in the space so that the distance (the value of the metric) between points of the same color does not belong to a given set of positive real numbers (the set of forbidden distances). New bounds for the chromatic number are obtained for the case in which the space is $\mathbb R^n$ with a metric generated by some norm (in particular, $l_p$) and the set of forbidden distances either is finite or forms a lacunary sequence.
Keywords: chromatic number, measurable chromatic number, coloring with forbidden distances, lacunary sequence, independence member of a graph, polyhedron, Diophantine approximation.
Received: 06.07.2005
Revised: 18.08.2006
English version:
Mathematical Notes, 2007, Volume 81, Issue 5, Pages 656–664
DOI: https://doi.org/10.1134/S0001434607050112
Bibliographic databases:
UDC: 519.174
Language: Russian
Citation: N. G. Moshchevitin, A. M. Raigorodskii, “Colorings of the Space $\mathbb R^n$ with Several Forbidden Distances”, Mat. Zametki, 81:5 (2007), 733–743; Math. Notes, 81:5 (2007), 656–664
Citation in format AMSBIB
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    • This publication is cited in the following 17 articles:
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