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Mat. Sb., 2009, Volume 200, Number 12, Pages 63–80 (Mi msb6373)  

This article is cited in 11 scientific papers (total in 11 papers)

On the Ramsey numbers for complete distance graphs with vertices in $\{0,1\}^n$

K. A. Mikhailov, A. M. Raigorodskii

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: A new problem of Ramsey type is posed for complete distance graphs in $\mathbb R^n$ with vertices in the Boolean cube. This problem is closely related to the classical Nelson-Erdős-Hadwiger problem on the chromatic number of a space. Several quite sharp estimates are obtained for certain numerical characteristics that appear in the framework of the problem.
Bibliography: 15 titles.

Keywords: Ramsey numbers, distance graphs, chromatic number.
Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/sm6373

Full text: PDF file (580 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2009, 200:12, 1789–1806

Bibliographic databases:

UDC: 519.112.4+519.174
MSC: Primary 05C55; Secondary 05C15, 05C80
Received: 04.06.2008

Citation: K. A. Mikhailov, A. M. Raigorodskii, “On the Ramsey numbers for complete distance graphs with vertices in $\{0,1\}^n$”, Mat. Sb., 200:12 (2009), 63–80; Sb. Math., 200:12 (2009), 1789–1806

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. M. E. Zhukovskii, “On a sequence of random distance graphs subject to the zero-one law”, Problems Inform. Transmission, 47:3 (2011), 251–268  mathnet  crossref  mathscinet  isi
    2. M. E. Zhukovskii, “A weak zero-one law for sequences of random distance graphs”, Sb. Math., 203:7 (2012), 1012–1044  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. M. E. Zhukovskii, “On the Probability of the Occurrence of a Copy of a Fixed Graph in a Random Distance Graph”, Math. Notes, 92:6 (2012), 756–766  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    4. S. N. Popova, “Zero-one law for random distance graphs with vertices in $\{-1,0,1\}^n$”, Problems Inform. Transmission, 50:1 (2014), 57–78  mathnet  crossref  isi
    5. L. I. Bogolyubskii, A. S. Gusev, M. M. Pyaderkin, A. M. Raigorodskii, “Independence numbers and chromatic numbers of random subgraphs in some sequences of graphs”, Dokl. Math., 90:1 (2014), 462–465  crossref  crossref  mathscinet  zmath  isi  elib  elib  scopus
    6. A. S. Gusev, “New Upper Bound for the Chromatic Numberof a Random Subgraph of a Distance Graph”, Math. Notes, 97:3 (2015), 326–332  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    7. L. I. Bogolubsky, A. S. Gusev, M. M. Pyaderkin, A. M. Raigorodskii, “Independence numbers and chromatic numbers of the random subgraphs of some distance graphs”, Sb. Math., 206:10 (2015), 1340–1374  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    8. Ph. A. Pushnyakov, “A new estimate for the number of edges in induced subgraphs of a special distance graph”, Problems Inform. Transmission, 51:4 (2015), 371–377  mathnet  crossref  isi  elib
    9. M. M. Pyaderkin, “Independence Numbers of Random Subgraphs of a Distance Graph”, Math. Notes, 99:2 (2016), 312–319  mathnet  crossref  crossref  mathscinet  isi  elib
    10. Ph. Pushnyakov, “On the Number of Edges in Induced Subgraphs of a Special Distance Graph”, Math. Notes, 99:4 (2016), 545–551  mathnet  crossref  crossref  mathscinet  isi  elib
    11. D. A. Zakharov, A. M. Raigorodskii, “Clique Chromatic Numbers of Intersection Graphs”, Math. Notes, 105:1 (2019), 137–139  mathnet  crossref  crossref  isi  elib
  • Математический сборник Sbornik: Mathematics (from 1967)
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