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Improved Frankl–Rödl Theorem and Some of Its Geometric Consequences

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Abstract

We substantially improve a presently known explicit exponentially growing lower bound on the chromatic number of a Euclidean space with forbidden equilateral triangle. Furthermore, we improve an exponentially growing lower bound on the chromatic number of distance graphs with large girth. These refinements are obtained by improving known upper bounds on the product of cardinalities of two families of homogeneous subsets with one forbidden cross-intersection.

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Authors and Affiliations

  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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Original Russian Text © A.A. Sagdeev, 2018, published in Problemy Peredachi Informatsii, 2018, Vol. 54, No. 2, pp. 45–72.

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

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Sagdeev, A.A. Improved Frankl–Rödl Theorem and Some of Its Geometric Consequences. Probl Inf Transm 54, 139–164 (2018). https://doi.org/10.1134/S0032946018020047

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