Nodes of large degree in random trees and forests

We study the asymptotic behaviour 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 ENk,n and asymptotically Poisson distributed if ENk,n C > 0. If ENk,n 0, then the distribution degenerates. The same holds for rooted, unlabeled trees and forests.

• Type: Journal
• Year: 2006
• Where: RSA
• Authors: Bernhard Gittenberger
• Keywords: Asymptotic Behaviour, Random Trees, RSA 2006, Tree Size