We show that a random labeled n-vertex graph almost surely contains isomorphic copies of almost all labeled n-vertex trees, in two senses. In the first sense, the probability of each edge occurring in the graph diminishes as n increases, and the set of trees referred to as "almost all" depends on the random graph. In the other sense, the probability of an edge occurring is fixed, and the releva...

We study the broadcasting problem when underlying tree is a random recursive tree. The root of has bit value assigned. Every other vertex same as its parent with probability 1?q and opposite q, where q?[0,1]. consists in estimating upon observing unlabeled tree, together associated every vertex. In more difficult version problem, observed but only values leaves are observed. When uniform both v...