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Matematicheskie Zametki, 2010, Volume 87, Issue 3, Pages 417–428
DOI: https://doi.org/10.4213/mzm5187 (Mi mzm5187) 		 
This article is cited in 10 scientific papers (total in 10 papers)

Distance Graphs with Large Chromatic Number and without Large Cliques

A. M. Raigorodskii, O. I. Rubanov

M. V. Lomonosov Moscow State University
Full-text PDF (563 kB) Citations (10)
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DOI: https://doi.org/10.4213/mzm5187
Abstract: The present paper is devoted to the study of the properties of distance graphs in Euclidean space. We prove, in particular, the existence of distance graphs with chromatic number of exponentially large dimension and without cliques of dimension 6. In addition, under a given constraint on the cardinality of the maximal clique, we search for distance graphs with extremal large values of the chromatic number. The resulting estimates are best possible within the framework of the proposed method, which combines probabilistic techniques with the linear-algebraic approach.
Keywords: distance graph, chromatic number, clique, Stirling's formula, Euclidean space, probability space, random variable, expectation.
Received: 04.06.2008
English version:
Mathematical Notes, 2010, Volume 87, Issue 3, Pages 392–402
DOI: https://doi.org/10.1134/S0001434610030119
Bibliographic databases:
Document Type: Article
UDC: 519.174
Language: Russian
Citation: A. M. Raigorodskii, O. I. Rubanov, “Distance Graphs with Large Chromatic Number and without Large Cliques”, Mat. Zametki, 87:3 (2010), 417–428; Math. Notes, 87:3 (2010), 392–402
Citation in format AMSBIB
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    • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические заметки Mathematical Notes
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