The 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 the size of the binary tree, but also its height and fringe thickness (the difference between the length of a shortest root-to-leaf path and the height). We characterize the maximum path length binary trees of a given height, size, and fringe thickness. Using this characterization, we give an algorithm to find the maximum path length binary trees of a given size and fringe thickness.