Fringe thickness and maximum path length of binary trees

AbstractWe show how to compute the maximum path length of binary trees with a given size and a given fringe thickness (the difference in length between a longest and a shortest root-to-leaf path). We demonstrate that the key to finding the maximum path length binary trees with size N and fringe thickness Δ is the height hΔ, N = ⌜log2((N + 1)(2Δ − 1)/Δ)⌝. First we show that trees with height hδ, N exist. Then we show that the maximum path length trees have height hΔ, N − 1, hΔ, N, or hΔ, N + 1