The Distribution of Patterns in Random Trees

Let Tn denote the set of unrooted labeled trees of size n and let M be a particular (finite, unlabeled) tree. Assuming that every tree of Tn is equally likely, it is shown that the limiting distribution as n goes to infinity of the number of occurrences of M as an induced subtree is asymptotically normal with mean value and variance asymptotically equivalent to

• Type: Journal
• Year: 2008
• Where: CPC
• Authors: Frédéric Chyzak, Michael Drmota, Thomas Klausner, Gerard Kok
• Keywords: CPC 2008, Infinity, Tree, Unrooted Labeled Trees