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Mat. Sb., 2014, Volume 205, Number 9, Pages 97–120 (Mi msb8312)  

This article is cited in 16 scientific papers (total in 16 papers)

On the chromatic number of a space with forbidden equilateral triangle

A. E. Zvonarevab, A. M. Raigorodskiiab, D. V. Samirovb, A. A. Kharlamovaa

a M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
b Department of Innovations and High Technology, Moscow Institute of Physics and Technology

Abstract: We improve the Frankl-Rödl estimate for the product of the numbers of edges in uniform hypergraphs with forbidden cardinalities of the intersection of edges. By using this estimate, we obtain explicit bounds for the chromatic number of a space with forbidden monochromatic equilateral triangles.
Bibliography: 31 titles.

Keywords: hypergraph, systems of sets with forbidden intersections, Euclidean Ramsey theory, chromatic number of a space.

Funding Agency Grant Number
Russian Foundation for Basic Research 12-01-00683
Ministry of Education and Science of the Russian Federation МД-6277.2013.1
НШ-2519.2012.1

Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/sm8312

Full text: PDF file (697 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2014, 205:9, 1310–1333

Bibliographic databases:

UDC: 517.538
MSC: Primary 05C65; Secondary 05C15, 05D10
Received: 12.12.2013 and 14.04.2014

Citation: A. E. Zvonarev, A. M. Raigorodskii, D. V. Samirov, A. A. Kharlamova, “On the chromatic number of a space with forbidden equilateral triangle”, Mat. Sb., 205:9 (2014), 97–120; Sb. Math., 205:9 (2014), 1310–1333

Citation in format AMSBIB
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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. 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”, Proc. Steklov Inst. Math., 288 (2015), 94–104  mathnet  crossref  crossref  isi  elib  elib
    2. M. M. Pyaderkin, “On the stability of the Erdős-Ko-Rado theorem”, Dokl. Math., 91:3 (2015), 290–293  crossref  crossref  mathscinet  zmath  isi  elib  elib  scopus
    3. D. V. Samirov, A. M. Raigorodskii, “Ob odnoi zadache, svyazannoi s optimalnoi raskraskoi prostranstva bez odnotsvetnykh ravnobedrennykh treugolnikov”, Trudy Moskovskogo fiziko-tekhnicheskogo instituta, 7 (2015), 39–50  elib
    4. 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
    5. A. M. Raigorodskii, “Combinatorial geometry and coding theory*”, Fund. Inform., 145:3 (2016), 359–369  crossref  mathscinet  zmath  isi  scopus
    6. 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
    7. A. M. Raigorodskii, A. A. Sagdeev, “On the chromatic number of a space with a forbidden regular simplex”, Dokl. Math., 95:1 (2017), 15–16  crossref  crossref  mathscinet  zmath  isi  elib  elib  scopus
    8. A. Sagdeev, “The Chromatic Number of Space with Forbidden Regular Simplex”, Math. Notes, 102:4 (2017), 541–546  mathnet  crossref  crossref  mathscinet  isi  elib
    9. 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  elib  scopus
    10. 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
    11. 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
    12. 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
    13. A. Sagdeev, “On the Frankl–Rödl theorem”, Izv. Math., 82:6 (2018), 1196–1224  mathnet  crossref  crossref  adsnasa  isi  elib
    14. A. A. Sagdeev, “Exponentially Ramsey sets”, Problems Inform. Transmission, 54:4 (2018), 372–396  mathnet  crossref  isi  elib
    15. A. A. Sagdeev, “On a Frankl–Wilson Theorem”, Problems Inform. Transmission, 55:4 (2019), 376–395  mathnet  crossref  crossref  isi  elib
    16. Sagdeev A.A. Raigorodskii A.M., “On a Frankl-Wilson Theorem and Its Geometric Corollaries”, Acta Math. Univ. Comen., 88:3 (2019), 1029–1033  mathscinet  isi
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