Random cherry graphs

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.