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Teoriya Veroyatnostei i ee Primeneniya, 1974, Volume 19, Issue 4, Pages 740–754 (Mi tvp3977)  

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

On extreme metric parameters of a random graph, I

Yu. D. Burtin

Leningrad
Abstract: A random graph $G_n(t)$ is considered such that the edge between every pair of its vertices exists with the probability $p=1-e^{-t}$, $0<t<\infty$, independently from the other edges.
Let $L=[\log_{nt}n]$ be the integer part of $\log_{nt}n$. Then, uniformly in $t\ge(c_n \log n)/n$ $(\lim_{n\to\infty}c_n=\infty)$,
$$ \lim_{n\to\infty}\mathbf P(L+l\le d(G_n(t))\le L+2)=1, $$
where $d(G_n(t))$ denotes the diameter of the random graph. Thus the limit distribution of the diameter may be concentrated at at most two points.
Analogous propositions hold true for the radius and the cycle index of the random graph $G_n(t)$.
Received: 01.03.1973
English version:
Theory of Probability and its Applications, 1975, Volume 19, Issue 4, Pages 710–725
DOI: https://doi.org/10.1137/1119080
Bibliographic databases:
Language: Russian
Citation: Yu. D. Burtin, “On extreme metric parameters of a random graph, I”, Teor. Veroyatnost. i Primenen., 19:4 (1974), 740–754; Theory Probab. Appl., 19:4 (1975), 710–725
Citation in format AMSBIB
\Bibitem{Bur74}
\by Yu.~D.~Burtin
\paper On extreme metric parameters of a~random graph,~I
\jour Teor. Veroyatnost. i Primenen.
\yr 1974
\vol 19
\issue 4
\pages 740--754
\mathnet{http://mi.mathnet.ru/tvp3977}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=369168}
\zmath{https://zbmath.org/?q=an:0351.60012}
\transl
\jour Theory Probab. Appl.
\yr 1975
\vol 19
\issue 4
\pages 710--725
\crossref{https://doi.org/10.1137/1119080}
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  • https://www.mathnet.ru/eng/tvp/v19/i4/p740
  • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Теория вероятностей и ее применения Theory of Probability and its Applications
     
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