Random cherry graphs

TL;DR

This paper introduces a new randomized model of cherry trees, extending previous work, and embeds it into a time-dependent branching process to analyze its properties.

Contribution

It presents a substantially extended random analogue of the cherry tree model within a general time-dependent branching process framework.

Findings

New probabilistic model for cherry trees

Analysis of the model's growth dynamics

Connections to branching process theory

Abstract

Due to the popularity of randomly evolving graph processes, there exists a randomized version of many recursively defined graph models. This is also the case with the cherry tree, which was introduced by Buksz\'ar and Pr\'ekopa to improve Bonferroni type upper bounds on the probability of the union of random events. Here we consider a substantially extended random analogue of that model, embedding it into a general time dependent branching process.