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arXiv · 2308.06580

Universal rooted phylogenetic tree shapes and universal tanglegrams

Ann Clifton·Eva Czabarka·Kevin Liu·Sarah Loeb·Utku Okur·Laszlo Szekely·Kristina Wicke
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Abstract

We provide an $\Omega(n\log n) $ lower bound and an $O(n^2)$ upper bound for the smallest size of rooted binary trees (a.k.a. phylogenetic tree shapes), which are universal for rooted binary trees with $n$ leaves, i.e., contain all of them as induced binary subtrees. We explicitly compute the smallest universal trees for $n\leq 11$. We also provide an $\Omega(n^2) $ lower bound and an $O(n^4)$ upper bound for the smallest size of tanglegrams, which are universal for size $n$ tanglegrams, i.e., which contain all of them as induced subtanglegrams. Some of our results generalize to rooted $d$-ary trees and to $d$-ary tanglegrams.

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Ann Clifton, Eva Czabarka, Kevin Liu, Sarah Loeb, Utku Okur, Laszlo Szekely, Kristina Wicke. 2023-08-12. Universal rooted phylogenetic tree shapes and universal tanglegrams. https://arxiv.org/abs/2308.06580

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