caa a22 4500 378930478 CHVBK 20180305123628.0 cr unu---uuuuu 161128e20040801xx s 000 0 eng 10.1515/1569392041938767 doi (NATIONALLICENCE)gruyter-10.1515/1569392041938767 Pavlov Yu. L. Limit theorems for sizes of trees in the unlabelled graph of a random mapping [Elektronische Daten] [Yu. L. Pavlov] We find limit distributions of the maximum size of a tree and of the number of trees of given size in an unlabelled random forest consisting of N rooted trees and n non-root vertices provided that N, n → ∞ so that 0 < C 1 ≤ N / √n ≤ C 2 < ∞. With the use of these results, for the unlabelled graph of a random single-valued mapping of the set {1, 2, . . .,n} into itself we prove theorems on the limit behaviour of the maximum tree size and of the number of trees of size r as n → ∞ in the cases of fixed r and r/n 1/3 ≥ C 3 > 0. Copyright 2004, Walter de Gruyter Discrete Mathematics and Applications Walter de Gruyter 14/4(2004-08-01), 329-342 0924-9265 14:4<329 2004 14 dma https://doi.org/10.1515/1569392041938767 text/html Onlinezugriff via DOI 1 research article jats NATIONALLICENCE 856 40 https://doi.org/10.1515/1569392041938767 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Pavlov Yu. L. NATIONALLICENCE 773 0- Discrete Mathematics and Applications Walter de Gruyter 14/4(2004-08-01), 329-342 0924-9265 14:4<329 2004 14 dma CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-gruyter