The shape of random tanglegrams

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• 作者：Matjaž Konvalinka^a ; ¹ ; ^{matjaz.konvalinka@fmf.uni-lj.si" class="auth_mail" title="E-mail the corresponding author} ; Stephan Wagner^b ; ² ; ^{swagner@sun.ac.za" class="auth_mail" title="E-mail the corresponding author}
• 关键词：60C05
• 刊名：Advances in Applied Mathematics
• 出版年：2016
• 出版时间：July 2016
• 年：2016
• 卷：78
• 期：Complete
• 页码：76-93
• 全文大小：372 K

文摘

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.