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arXiv · 2501.13670

Reconstruction of caterpillar tanglegrams

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

A tanglegram consists of two rooted binary trees with the same number of leaves and a perfect matching between the leaves of the trees. Given a size-$n$ tanglegram, i.e., a tanglegram for two trees with $n$ leaves, a multiset of induced size-$(n-1)$ tanglegrams is obtained by deleting a pair of matched leaves in every possible way. Here, we analyze whether a size-$n$ tanglegram is uniquely encoded by this multiset of size-$(n-1)$ tanglegrams. We answer this question affirmatively in the case that at least one of the two trees of the tanglegram is a caterpillar tree.

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Ann Clifton, Eva Czabarka, Kevin Liu, Sarah Loeb, Utku Okur, Laszlo Szekely, Kristina Wicke. 2025-01-23. Reconstruction of caterpillar tanglegrams. https://arxiv.org/abs/2501.13670

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