2015/12/03 by Matjaž Konvalinka, Stephan Wagner, Konvalinka, Matjaž +1
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #Data Management and Algorithms #FOS: Mathematics #Topological and Geometric Data Analysis #math.CO
paper · pdf · doi:10.48550/arxiv.1512.01168
openalex publication_date 2015/12/03 · arxiv created 2016/04/07 · arxiv updated 2016/04/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A tanglegram consists of two binary rooted trees with the same number of leaves and a perfect matching between the leaves of the trees. We show that the two halves of a random tanglegram essentially look like two independently chosen random plane binary trees. This fact is used to derive a number of results on the shape of random tanglegrams, including theorems on the number of cherries and generally occurrences of subtrees, the root branches, the number of automorphisms, and the height. For each of these, we obtain limiting probabilities or distributions. Finally, we investigate the number of matched cherries, for which the limiting distribution is identified as well.