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Probl. Peredachi Inf., 2019, Volume 55, Issue 4, Pages 86–106 (Mi ppi2305)  
This article is cited in 1 scientific paper (total in 1 paper)

Large Systems

On a Frankl–Wilson Theorem

A. A. Sagdeev

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

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 $\mathbb{R}^n$ with a forbidden equilateral triangle and to the problem of chromatic numbers of distance graphs with large girth.

Keywords: distance graph, Frankl–Wilson theorem, Frankl–Rödl theorem, chromatic number, Euclidean Ramsey theory, girth.

Funding Agency Grant Number
Russian Foundation for Basic Research 18-01-00355_а
Ministry of Education and Science of the Russian Federation НШ-6760.2018.1
Simons Foundation
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.


DOI: https://doi.org/10.1134/S0134347519040041

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English version:
Problems of Information Transmission, 2019, 55:4, 376–395

Bibliographic databases:

UDC: 629.391.1 : 519.1
Received: 02.07.2019
Revised: 09.10.2019
Accepted:12.11.2019

Citation: A. A. Sagdeev, “On a Frankl–Wilson Theorem”, Probl. Peredachi Inf., 55:4 (2019), 86–106; Problems Inform. Transmission, 55:4 (2019), 376–395

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. B. Kupavskii, A. A. Sagdeev, “Ramsey theory in the $n$-space with Chebyshev metric”, Russian Math. Surveys, 75:5 (2020), 965–967  mathnet  crossref  crossref
    		• Проблемы передачи информации Problems of Information Transmission
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