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Tr. Mat. Inst. Steklova, 2015, Volume 288, Pages 109–119 (Mi tm3603)  

This article is cited in 10 scientific papers (total in 10 papers)

Improvements of the Frankl–Rödl theorem on the number of edges of a hypergraph with forbidden intersections, and their consequences in the problem of finding the chromatic number of a space with forbidden equilateral triangle

A. E. Zvonareva, A. M. Raigorodskiiba

a Department of Innovations and High Technology, Moscow Institute of Physics and Technology, Dolgoprudnyi, Russia
b Department of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia

Abstract: We survey the results (both old and new) related to the classical Frankl–Rödl theorem on the upper bound for the product of cardinalities of edge sets of two hypergraphs satisfying the condition that the intersection of any two edges of different hypergraphs cannot consist of a prescribed number of vertices. We also present corollaries to these results in the problem of finding the chromatic number of a space with a forbidden equilateral triangle with monochromatic vertices.

Funding Agency Grant Number
Russian Foundation for Basic Research 15-01-03530
Ministry of Education and Science of the Russian Federation МД-6277.2013.1
НШ-2964.2014.1


DOI: https://doi.org/10.1134/S0371968515010070

Full text: PDF file (228 kB)
References: PDF file   HTML file

English version:
Proceedings of the Steklov Institute of Mathematics, 2015, 288, 94–104

Bibliographic databases:

UDC: 519.179.1+519.174.7
Received in October 2014

Citation: A. E. Zvonarev, A. M. Raigorodskii, “Improvements of the Frankl–Rödl theorem on the number of edges of a hypergraph with forbidden intersections, and their consequences in the problem of finding the chromatic number of a space with forbidden equilateral triangle”, Geometry, topology, and applications, Collected papers. Dedicated to Professor Nikolai Petrovich Dolbilin on the occasion of his 70th birthday, Tr. Mat. Inst. Steklova, 288, MAIK Nauka/Interperiodica, Moscow, 2015, 109–119; Proc. Steklov Inst. Math., 288 (2015), 94–104

Citation in format AMSBIB
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\by A.~E.~Zvonarev, A.~M.~Raigorodskii
\paper Improvements of the Frankl--R\"odl theorem on the number of edges of a~hypergraph with forbidden intersections, and their consequences in the problem of finding the chromatic number of a~space with forbidden equilateral triangle
\inbook Geometry, topology, and applications
\bookinfo Collected papers. Dedicated to Professor Nikolai Petrovich Dolbilin on the occasion of his 70th birthday
\serial Tr. Mat. Inst. Steklova
\yr 2015
\vol 288
\pages 109--119
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm3603}
\crossref{https://doi.org/10.1134/S0371968515010070}
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\jour Proc. Steklov Inst. Math.
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\pages 94--104
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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. V. Bobu, A. E. Kupriyanov, “On chromatic numbers of close-to-Kneser distance graphs”, Problems Inform. Transmission, 52:4 (2016), 373–390  mathnet  crossref  isi  elib
    2. A. M. Raigorodskii, “Combinatorial geometry and coding theory”, Fundam. Inform., 145:3 (2016), 359–369  crossref  mathscinet  zmath  isi
    3. A. Sagdeev, “Lower Bounds for the Chromatic Numbers of Distance Graphs with Large Girth”, Math. Notes, 101:3 (2017), 515–528  mathnet  crossref  crossref  mathscinet  isi  elib
    4. A. Sagdeev, “The Chromatic Number of Space with Forbidden Regular Simplex”, Math. Notes, 102:4 (2017), 541–546  mathnet  crossref  crossref  mathscinet  isi  elib
    5. R. I. Prosanov, A. M. Raigorodskii, A. A. Sagdeev, “Improvements of the Frankl-Rodl theorem and geometric consequences”, Dokl. Math., 96:1 (2017), 336–338  crossref  crossref  mathscinet  zmath  isi  scopus
    6. A. V. Bobu, A. E. Kupriyanov, A. M. Raigorodskii, “On the number of edges of a uniform hypergraph with a range of allowed intersections”, Problems Inform. Transmission, 53:4 (2017), 319–342  mathnet  crossref  isi  elib
    7. R. I. Prosanov, “Upper Bounds for the Chromatic Numbers of Euclidean Spaces with Forbidden Ramsey Sets”, Math. Notes, 103:2 (2018), 243–250  mathnet  crossref  crossref  isi  elib
    8. A. M. Raigorodskii, A. A. Sagdeev, “On a bound in extremal combinatorics”, Dokl. Math., 97:1 (2018), 47–48  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  scopus
    9. A. A. Sagdeev, “Improved Frankl–Rödl theorem and some of its geometric consequences”, Problems Inform. Transmission, 54:2 (2018), 139–164  mathnet  crossref  isi  elib
    10. A. A. Sagdeev, “Exponentially Ramsey sets”, Problems Inform. Transmission, 54:4 (2018), 372–396  mathnet  crossref  isi
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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