Reducing Simply Generated Trees by Iterative Leaf Cutting

TL;DR

This paper analyzes a method for simplifying simply generated trees through iterative leaf removal, providing asymptotic and probabilistic results on the number of vertices removed after multiple iterations.

Contribution

It introduces a recursive model to quantify leaf removal effects, deriving asymptotic formulas and a central limit theorem for the number of deleted vertices.

Findings

Asymptotic formulas for mean and variance of deleted vertices

Central limit theorem for the distribution of deleted vertices

Recursive characterization of leaf removal process

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.