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 Probl. Peredachi Inf., 2018, Volume 54, Issue 2, Pages 45–72 (Mi ppi2266)

Large Systems

Improved Frankl–Rödl theorem and some of its geometric consequences

A. A. Sagdeev

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

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.

 Funding Agency Grant Number Russian Foundation for Basic Research 18-01-00355 Ministry of Education and Science of the Russian Federation ÍØ-6760.2018.1 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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English version:
Problems of Information Transmission, 2018, 54:2, 139–164

Bibliographic databases:

UDC: 621.391.1+519.1
Revised: 27.12.2017

Citation: A. A. Sagdeev, “Improved Frankl–Rödl theorem and some of its geometric consequences”, Probl. Peredachi Inf., 54:2 (2018), 45–72; Problems Inform. Transmission, 54:2 (2018), 139–164

Citation in format AMSBIB
\Bibitem{Sag18} \by A.~A.~Sagdeev \paper Improved Frankl--R\"odl theorem and some of its geometric consequences \jour Probl. Peredachi Inf. \yr 2018 \vol 54 \issue 2 \pages 45--72 \mathnet{http://mi.mathnet.ru/ppi2266} \elib{http://elibrary.ru/item.asp?id=35768874} \transl \jour Problems Inform. Transmission \yr 2018 \vol 54 \issue 2 \pages 139--164 \crossref{https://doi.org/10.1134/S0032946018020047} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000438828500004} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85049976987} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. A. A. Sagdeev, “Exponentially Ramsey sets”, Problems Inform. Transmission, 54:4 (2018), 372–396
2. A. A. Sagdeev, “O khromaticheskikh chislakh, sootvetstvuyuschikh eksponentsialno ramseevskim mnozhestvam”, Kombinatorika i teoriya grafov. X, Zap. nauchn. sem. POMI, 475, POMI, SPb., 2018, 174–189
3. L. I. Bogolubsky, A. M. Raigorodskii, “A Remark on Lower Bounds for the Chromatic Numbers of Spaces of Small Dimension with Metrics $\ell_1$ and $\ell_2$”, Math. Notes, 105:2 (2019), 180–203
4. Ph. A. Pushnyakov, “The Number of Edges in Induced Subgraphs of Some Distance Graphs”, Math. Notes, 105:4 (2019), 582–591
5. R. I. Prosanov, “Counterexamples to Borsuk's Conjecture with Large Girth”, Math. Notes, 105:6 (2019), 874–880
6. A. A. Sagdeev, “On the Partition of an Odd Number into Three Primes in a Prescribed Proportion”, Math. Notes, 106:1 (2019), 98–107
7. F. A. Pushnyakov, A. M. Raigorodskii, “Otsenka chisla reber v osobykh podgrafakh nekotorogo distantsionnogo grafa”, Matem. zametki, 107:2 (2020), 286–298
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