Uniform attachment with freezing

TL;DR

This paper investigates how freezing vertices in a recursive tree model affects the tree's height, providing insights into structural changes caused by freezing.

Contribution

It introduces a modified recursive tree model with freezing and analyzes its impact on the height, a novel aspect not previously studied.

Findings

Freezing vertices alters the height growth of recursive trees.

The model demonstrates different height scaling behaviors with freezing.

Freezing leads to a phase transition in the tree's structural properties.

Abstract

In the classical model of random recursive trees, trees are recursively built by attaching new vertices to old ones. What happens if vertices are allowed to freeze, in the sense that new vertices cannot be attached to already frozen ones? We are interested in the impact of freezing on the height of such trees.