Maximal path length of binary trees

Abstract

We further refine the bounds on the path length of binary trees of a given size by considering not only their sizes, but also their heights and fringe thicknesses (the difference between the length of their shortest root-to-leaf paths and their heights). We characterize the maximum-path-length binary trees of a given height, size, and fringe thickness, and using this characterization, we give an algorithm to find the maximum-path-length binary trees of a given size and fringe thickness. The proof of the main result is based on two new tree transformations that preserve the height, size, and fringe thickness.