2017/05/26 by Miklós Bóna, Bona, Miklos
Computer Science · Mathematics · #05A05 #05A15 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.1705.09688
openalex publication_date 2017/05/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In a rooted tree, we call a vertex \em balanced if it is at equal distance from all its descendant leaves. We count balanced vertices in three different tree varieties. For decreasing binary trees, we can prove that the probability that a vertex chosen uniformly at random from the set of all trees of a given size is balanced is monotone decreasing.