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Matematicheskie Zametki, 2012, Volume 91, Issue 3, Pages 422–431
DOI: https://doi.org/10.4213/mzm8602 (Mi mzm8602) 		 
On the Chromatic Number for a Set of Metric Spaces

I. M. Mitricheva (Shitova)

M. V. Lomonosov Moscow State University
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DOI: https://doi.org/10.4213/mzm8602
Abstract: We study the problem of finding the chromatic number of a metric space with a forbidden distance. Using the linear-algebraic technique in combinatorics and convex optimization methods, we obtain a set of new estimates and observe the change of the asymptotic lower bound for the chromatic number of Euclidean space under the continuous change of the metric from $l_1$ to $l_2$.
Keywords: metric space with a forbidden distance, chromatic number, convex optimization, Euclidean space, graph, Karush–Kuhn–Tucker theorem, Lagrange function.
Received: 15.04.2009
English version:
Mathematical Notes, 2012, Volume 91, Issue 3, Pages 399–408
DOI: https://doi.org/10.1134/S0001434612030091
Bibliographic databases:
Document Type: Article
UDC: 514.177.2+519.157+519.174.7
Language: Russian
Citation: I. M. Mitricheva (Shitova), “On the Chromatic Number for a Set of Metric Spaces”, Mat. Zametki, 91:3 (2012), 422–431; Math. Notes, 91:3 (2012), 399–408
Citation in format AMSBIB
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