This article is cited in 9 papers

The emergence of a giant tree in a random forest

I. A. Cheplyukova


Abstract: We consider random forests consisting of $N$ trees of a simply generated family of rooted trees with $n$ non-root vertices. For these forests, we investigate the conditions when the giant tree comes into existence in the random forest and demonstrate that the giant component can occur only in the case where $N,n\to\infty $ so that $n/N^2\to\infty$.
This research was supported by the Russian Foundation for Basic Research, grant 97–01–00065.

UDC: 519.2

Received: 22.08.1997

DOI: 10.4213/dm408

 English version: Discrete Mathematics and Applications, 1998, 8:1, 17–33

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