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Mat. Zametki, 2012, Volume 92, Issue 6, Pages 844–855 (Mi mz9114)  

This article is cited in 3 scientific papers (total in 3 papers)

On the Probability of the Occurrence of a Copy of a Fixed Graph in a Random Distance Graph

M. E. Zhukovskii

M. V. Lomonosov Moscow State University

Abstract: The threshold probability of the occurrence of a copy of a balanced graph in a random distance graph is obtained. The technique used by P. Erdős and A. Rényi for determining the threshold probability for the classical random graph could not be applied in the model under consideration. In this connection, a new method for deriving estimates of the number of copies of a balanced graph in a complete distance graph is developed.

Keywords: random distance graph, complete distance graph, balanced graph, threshold probability, Erdős–Rényi theorem on threshold probability, Stirling's formula

DOI: https://doi.org/10.4213/mzm9114

Full text: PDF file (524 kB)
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English version:
Mathematical Notes, 2012, 92:6, 756–766

Bibliographic databases:

UDC: 519.175.4
Received: 16.02.2011

Citation: M. E. Zhukovskii, “On the Probability of the Occurrence of a Copy of a Fixed Graph in a Random Distance Graph”, Mat. Zametki, 92:6 (2012), 844–855; Math. Notes, 92:6 (2012), 756–766

Citation in format AMSBIB
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  • https://doi.org/10.4213/mzm9114
  • http://mi.mathnet.ru/eng/mz/v92/i6/p844

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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, A. M. Raigorodskii, “Random graphs: models and asymptotic characteristics”, Russian Math. Surveys, 70:1 (2015), 33–81  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. A. V. Burkin, “Small subgraphs in random distance graphs”, Theory Probab. Appl., 60:3 (2016), 367–382  mathnet  crossref  crossref  mathscinet  isi  elib
    3. A. V. Burkin, M. E. Zhukovskii, “Small subgraphs and their extensions in a random distance graph”, Sb. Math., 209:2 (2018), 163–186  mathnet  crossref  crossref  adsnasa  isi  elib
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