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On a Frankl-Wilson Theorem

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Abstract

We derive an analog of the Frankl-Wilson theorem on independence numbers of some distance graphs. The obtained results are applied to the problem of the chromatic number of a space ℝn with a forbidden equilateral triangle and to the problem of chromatic numbers of distance graphs with large girth.

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Acknowledgement

The author is grateful to Valentina Rybnikova for valuable assistance in organizing the computer calculations.

Funding

The research was supported in part by the Russian Foundation for Basic Research, project no. 18-01-00355; the President of the Russian Federation Council for State Support of Leading Scientific Schools, grant no. NSh-6760.2018.1; and the Simons Foundation.

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  1. Laboratory of Advanced Combinatorics and Network Applications, Moscow Institute of Physics and Technology (State University), Moscow, Russia

    A. A. Sagdeev

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  1. A. A. Sagdeev
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Correspondence to A. A. Sagdeev.

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Russian Text © The Author(s), 2019, published in Problemy Peredachi Informatsii, 2019, Vol. 55, No. 4, pp. 86–106.

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Sagdeev, A.A. On a Frankl-Wilson Theorem. Probl Inf Transm 55, 376–395 (2019). https://doi.org/10.1134/S0032946019040045

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  • DOI: https://doi.org/10.1134/S0032946019040045

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