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Mat. Zametki, 2021, Volume 109, Issue 5, Pages 723–733 (Mi mz12864)  

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

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).


DOI: https://doi.org/10.4213/mzm12864

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English version:
Mathematical Notes, 2021, 109:5, 727–734

Bibliographic databases:

UDC: 519.173.5+519.174.7
Received: 09.08.2020

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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