Geodesic
Number of maximal rooted trees in uniform attachment model via stochastic approximation
Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 3 (2022), pp. 27-34

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We study the asymptotic behavior of the number of maximal trees in a uniform attachment model. In our model, we consider a sequence of graphs built by the following recursive rule. We start with the complete graph on $m+1$ vertices, $m>1$. Then on the $n+1$ step, we add vertex $n+1$ and draw $m$ edges from it to different vertices, chosen uniformly from $1,\ldots,n$. We prove the convergence speed for the number of maximal trees in such a model using the stochastic approximation technique.
Keywords: random graphs, uniform attachment, stochastic approximation. 
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     author = {Yu. A. Malyshkin},
     title = {Number of maximal rooted trees in uniform attachment model via stochastic approximation},
     journal = {Vestnik Tverskogo gosudarstvennogo universiteta. Seri\^a Prikladna\^a matematika},
     pages = {27--34},
     publisher = {mathdoc},
     number = {3},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTPMK_2022_3_a1/}
}
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Yu. A. Malyshkin. Number of maximal rooted trees in uniform attachment model via stochastic approximation. Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 3 (2022), pp. 27-34. http://geodesic.mathdoc.fr/item/VTPMK_2022_3_a1/