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Izv. RAN. Ser. Mat., 2018, Volume 82, Issue 6, Pages 128–157 (Mi izv8630)  

This article is cited in 7 scientific papers (total in 7 papers)

On the Frankl–Rödl theorem

A. Sagdeev

Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow region

Abstract: In this paper we considerably strengthen the currently known explicit exponential lower bound for the chromatic number of a Euclidean space with a forbidden regular simplex. We also strengthen the exponential lower bound for the chromatic numbers of distance graphs with large girth.

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

Funding Agency Grant Number
Russian Foundation for Basic Research 18-01-00355
Ministry of Education and Science of the Russian Federation НШ-6760.2018.1
This paper was written with the partial financial support of the Russian Foundation for Basic Research (grant no. 18-01-00355) and that of the grant in support of leading scientific schools no. NSh-6760.2018.1.


DOI: https://doi.org/10.4213/im8630

Full text: PDF file (786 kB)
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English version:
Izvestiya: Mathematics, 2018, 82:6, 1196–1224

Bibliographic databases:

UDC: 517
MSC: 05C15, 05C12, 05D10
Received: 18.11.2016
Revised: 09.04.2018

Citation: A. Sagdeev, “On the Frankl–Rödl theorem”, Izv. RAN. Ser. Mat., 82:6 (2018), 128–157; Izv. Math., 82:6 (2018), 1196–1224

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  • http://mi.mathnet.ru/eng/izv8630
  • https://doi.org/10.4213/im8630
  • http://mi.mathnet.ru/eng/izv/v82/i6/p128

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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  mathnet  crossref  isi  elib
    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  mathnet
    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  mathnet  crossref  crossref  isi  elib
    4. Ph. A. Pushnyakov, “The Number of Edges in Induced Subgraphs of Some Distance Graphs”, Math. Notes, 105:4 (2019), 582–591  mathnet  crossref  crossref  isi  elib
    5. R. I. Prosanov, “Counterexamples to Borsuk's Conjecture with Large Girth”, Math. Notes, 105:6 (2019), 874–880  mathnet  crossref  crossref  isi  elib
    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  mathnet  crossref  crossref  isi  elib
    7. F. A. Pushnyakov, A. M. Raigorodskii, “Otsenka chisla reber v osobykh podgrafakh nekotorogo distantsionnogo grafa”, Matem. zametki, 107:2 (2020), 286–298  mathnet  crossref
  • Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya Izvestiya: Mathematics
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