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Mat. Zametki, 2014, Volume 96, Issue 1, Pages 138–147 (Mi mz10352)  

This article is cited in 8 scientific papers (total in 8 papers)

New Upper Bounds for the Independence Numbers of Graphs with Vertices in $\{-1,0,1\}^n$ and Their Applications to Problems of the Chromatic Numbers of Distance Graphs

E. I. Ponomarenkoa, A. M. Raigorodskiiba

a Moscow Institute of Physics and Technology (State University)
b M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: Upper bounds for the independence numbers in the graphs with vertices at $\{-1, 0,1\}^n$ are improved. Their applications to problems of the chromatic numbers of distance graphs are studied.

Keywords: graph, hypergraph, independence number, chromatic number, distance graph, Hamming distance, Nelson–Erdős–Hadwiger problem.

DOI: https://doi.org/10.4213/mzm10352

Full text: PDF file (532 kB)
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English version:
Mathematical Notes, 2014, 96:1, 140–148

Bibliographic databases:

UDC: 519.17
Received: 08.08.2013
Revised: 26.11.2013

Citation: E. I. Ponomarenko, A. M. Raigorodskii, “New Upper Bounds for the Independence Numbers of Graphs with Vertices in $\{-1,0,1\}^n$ and Their Applications to Problems of the Chromatic Numbers of Distance Graphs”, Mat. Zametki, 96:1 (2014), 138–147; Math. Notes, 96:1 (2014), 140–148

Citation in format AMSBIB
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  • http://mi.mathnet.ru/eng/mz/v96/i1/p138

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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. 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
    3. L. E. Shabanov, “Turán type results for distance graphs in infinitesimal plane layer”, J. Math. Sci. (N. Y.), 236:5 (2019), 554–578  mathnet  crossref
    4. P. Frankl, A. Kupayskii, “Erdös-Ko-Rado theorem for $\{0,\pm 1\}$-vectors”, J. Comb. Theory Ser. A, 155 (2018), 157–179  crossref  mathscinet  zmath  isi  scopus
    5. P. Frankl, “An exact result for $(0,\pm 1)$-vectors”, Optim. Lett., 12:5 (2018), 1011–1017  crossref  mathscinet  zmath  isi  scopus
    6. P. Frankl, A. Kupavskii, “Families of vectors without antipodal pairs”, Stud. Sci. Math. Hung., 55:2 (2018), 231–237  crossref  mathscinet  zmath  isi  scopus
    7. A. M. Raigorodskii, T. V. Trukhan, “On the chromatic numbers of some distance graphs”, Dokl. Math., 98:2 (2018), 515–517  mathnet  crossref  crossref  zmath  isi  elib  scopus
    8. O. A. Kostina, “On Lower Bounds for the Chromatic Number of Spheres”, Math. Notes, 105:1 (2019), 16–27  mathnet  crossref  crossref  isi  elib
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