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Sbornik: Mathematics, 2014, Volume 205, Issue 9, Pages 1310–1333
DOI: https://doi.org/10.1070/SM2014v205n09ABEH004419 (Mi sm8312) 		 
This article is cited in 17 scientific papers (total in 17 papers)

On the chromatic number of a space with forbidden equilateral triangle

A. E. Zvonarevab, A. M. Raigorodskiiab, D. V. Samirovb, A. A. Kharlamovaa

a M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
b Department of Innovations and High Technology, Moscow Institute of Physics and Technology
English version PDF (631 kB) Citations (17)
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DOI: https://doi.org/10.1070/SM2014v205n09ABEH004419
Abstract: We improve the Frankl-Rödl estimate for the product of the numbers of edges in uniform hypergraphs with forbidden cardinalities of the intersection of edges. By using this estimate, we obtain explicit bounds for the chromatic number of a space with forbidden monochromatic equilateral triangles.
Bibliography: 31 titles.
Keywords: hypergraph, systems of sets with forbidden intersections, Euclidean Ramsey theory, chromatic number of a space.
Funding agency Grant number
Russian Foundation for Basic Research 12-01-00683
Ministry of Education and Science of the Russian Federation МД-6277.2013.1
НШ-2519.2012.1
Received: 12.12.2013 and 14.04.2014
Russian version:
Matematicheskii Sbornik, 2014, Volume 205, Number 9, Pages 97–120
DOI: https://doi.org/10.4213/sm8312
Bibliographic databases:
Document Type: Article
UDC: 517.538
MSC: Primary 05C65; Secondary 05C15, 05D10
Language: English
Original paper language: Russian
Citation: A. E. Zvonarev, A. M. Raigorodskii, D. V. Samirov, A. A. Kharlamova, “On the chromatic number of a space with forbidden equilateral triangle”, Mat. Sb., 205:9 (2014), 97–120; Sb. Math., 205:9 (2014), 1310–1333
Citation in format AMSBIB
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  • https://doi.org/10.1070/SM2014v205n09ABEH004419
  • https://www.mathnet.ru/eng/sm/v205/i9/p97
    • This publication is cited in the following 17 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Russian version PDF:197
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    References:89
    First page:60
     
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