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This article is cited in 3 scientific papers (total in 3 papers)
The cycle structure of a random nonhomogeneous hypergraph on the subcritical stage of evolution
A. V. Shapovalov
Abstract:
We consider a random nonhomogeneous hypergraph on $n$ vertices with $M=M(n)$ edges, $M_i=M_i(n)$ edges consist of $i$ vertices,
\begin{gather*}
\lim_{n\to\infty}M_i/M=c_i,\quad c_i\ge0,\quad i=0,1,\dots,m,\\
c_0+c_1+\dots+c_m=1,\quad M=M_0+M_1+\dots+M_m.
\end{gather*}
For each edge, vertices are chosen by random and equiprobable sampling with replacement out of $n$ vertices. Under the condition that $n\to\infty$ and
$$
0<\lim_{n\to\infty}\frac Mn<\Biggl(\sum_{i=2}^mc_ii(i-1)\Biggr)^{-1}
$$
we show that the probability that the random hypergraph consists of hypertrees and components with one cycle tends to one. Similar results for random graphs and random homogeneous hypergraphs have been obtained earlier.
Received: 10.06.2005
Citation:
A. V. Shapovalov, “The cycle structure of a random nonhomogeneous hypergraph on the subcritical stage of evolution”, Diskr. Mat., 19:4 (2007), 52–69; Discrete Math. Appl., 17:5 (2007), 475–493
Linking options:
https://www.mathnet.ru/eng/dm977https://doi.org/10.4213/dm977 https://www.mathnet.ru/eng/dm/v19/i4/p52
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Abstract page: | 461 | Full-text PDF : | 196 | References: | 44 | First page: | 3 |
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