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Matematicheskie Zametki, 2021, Volume 109, Issue 5, Pages 723–733
DOI: https://doi.org/10.4213/mzm12864 (Mi mzm12864) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Chromatic Numbers of Distance Graphs without Short Odd Cycles in Rational Spaces

Yu. A. Demidovich, M. E. Zhukovskii

Moscow Institute of Physics and Technology (National Research University), Dolgoprudny, Moscow Region
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DOI: https://doi.org/10.4213/mzm12864
Abstract: We prove the existence in rational spaces of distance graphs without short odd cycles whose chromatic number increases exponentially with the dimension of the space.
Keywords: chromatic number, linear-algebraic method, distance graph, graph girth.
Funding agency Grant number
Russian Foundation for Basic Research 18-01-00355
Ministry of Education and Science of the Russian Federation НШ-2540.2020.1
075-15-2019-1926
The proof of Theorem 3 was supported by the Russian Foundation for Basic Research (science grant no. 18-01-00355) and by the program “Leading Scientific Schools” (grant no. NSh-2540.2020.1). The proof of Corollary 1 was supported by the Grant of the Government of the Russian Federation for the state support of scientific research supervised by leading scientists (agreement no. 075-15-2019-1926).
Received: 09.08.2020
English version:
Mathematical Notes, 2021, Volume 109, Issue 5, Pages 727–734
DOI: https://doi.org/10.1134/S0001434621050060
Bibliographic databases:
Document Type: Article
UDC: 519.173.5+519.174.7
Language: Russian
Citation: Yu. A. Demidovich, M. E. Zhukovskii, “Chromatic Numbers of Distance Graphs without Short Odd Cycles in Rational Spaces”, Mat. Zametki, 109:5 (2021), 723–733; Math. Notes, 109:5 (2021), 727–734
Citation in format AMSBIB
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  • https://doi.org/10.4213/mzm12864
  • https://www.mathnet.ru/eng/mzm/v109/i5/p723
    • This publication is cited in the following 1 articles:
    1. V. S. Karas, A. M. Raigorodskii, “On Ramsey numbers for arbitrary sequences of graphs”, Dokl. Math., 105:1 (2022), 14–17  mathnet  crossref  crossref  mathscinet  elib
    Citing articles in Google Scholar: Russian citations, English citations
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