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| Hauptverfasser: | , , , , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2501.13670 |
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| _version_ | 1866913992668086272 |
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| author | Clifton, Ann Czabarka, Eva Liu, Kevin Loeb, Sarah Okur, Utku Szekely, Laszlo Wicke, Kristina |
| author_facet | Clifton, Ann Czabarka, Eva Liu, Kevin Loeb, Sarah Okur, Utku Szekely, Laszlo Wicke, Kristina |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_13670 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Reconstruction of caterpillar tanglegrams Clifton, Ann Czabarka, Eva Liu, Kevin Loeb, Sarah Okur, Utku Szekely, Laszlo Wicke, Kristina Combinatorics 05C05, 05C10, 05C60 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. |
| title | Reconstruction of caterpillar tanglegrams |
| topic | Combinatorics 05C05, 05C10, 05C60 |
| url | https://arxiv.org/abs/2501.13670 |