Reducing Simply Generated Trees by Iterative Leaf Cutting

Abstract

We consider a procedure to reduce simply generated trees by iteratively removing all leaves. In the context of this reduction, we study the number of vertices that are deleted after applying this procedure a fixed number of times by using an additive tree parameter model combined with a recursive characterization.Our results include asymptotic formulas for mean and variance of this quantity as well as a central limit theorem.2010 Mathematics Subject Classification. 05A15; 05A16, 05C05, 60C05.