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Matematicheskie Zametki, 2012, Volume 92, Issue 6, Pages 844–855
DOI: https://doi.org/10.4213/mzm9114 (Mi mzm9114) 		 
This article is cited in 5 scientific papers (total in 5 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
Full-text PDF (524 kB) Citations (5)
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DOI: https://doi.org/10.4213/mzm9114
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.
Received: 16.02.2011
English version:
Mathematical Notes, 2012, Volume 92, Issue 6, Pages 756–766
DOI: https://doi.org/10.1134/S000143461211020X
Bibliographic databases:
Document Type: Article
UDC: 519.175.4
Language: Russian
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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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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