PC Seminar: Maximal local mean and local density of a tree

Abstract: Given a tree T and a subtree S, the local mean at S can be defined as the average order of the subtrees containing S. Properties of subtrees that attains maximal local mean are then of interest. It will be shown that such maximal subtrees have at most one leaf with degree greater than 2. Local density is a normalization of local mean so that one can compare subtrees of different orders. I will discuss some basic properties of local densities such as upper/lower bounds.

This is a seminar in our seminar series on Probability and Combinatorics (PC).