The binary search tree or Quicksort is the most used of all sorting algorithm, since it is both fast and simple. The random recursive tree is another extensively studied random tree. We have examined fringe trees in these two types of random trees, since the study of such subtrees appears to be an effective approach towards defining characteristics also of the whole tree. By using a representat...

A tree is called k-decomposable if it has a spanning forest whose components are all of size k. In this paper, we study the number of k-decomposable trees in families of increasing trees, i.e. labeled trees in which the unique path from the root to an arbitrary vertex forms an increasing sequence. Functional equations for the corresponding counting series are provided, yielding asymptotic or ev...

In a recent paper, Shah and Zaman proposed the rumor center as an effective rumor source estimator for rumor spreading on random graphs. They proved for a very general random tree model that the detection probability remains positive as the number of nodes to which the rumor has spread tends to infinity. Moreover, they derived explicit asymptotic formulas for the detection probability of random...