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Abstract

We study the asymptotic behavior of the number Nk,n of nodes of given degree k in unlabeled random trees, when the tree size n and the node degree k both tend to infinity. It is shown that Nk,n is asymptotically normal if equation image and asymptotically Poisson distributed if equation image. If equation image, then the distribution degenerates. The same holds for rooted, unlabeled trees and forests. © 2006 Wiley Periodicals, Inc. Random Struct. Alg., 2006