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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.23309 |
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Table of Contents:
- The $\textit{$m$-deck}$ of an $n$-vertex graph is the multiset of unlabeled induced subgraphs with $m$ vertices. Caterpillars are trees in which all nonleaf vertices lie on a single path. We prove for $n\ge48$ that any $n$-vertex caterpillar is reconstructible (up to isomorphism) from its $m$-deck when $m>n/2$. The result is sharp, since for $n\ge6$ there are two $n$-vertex caterpillars having the same $\lfloor n/2 \rfloor$-deck. Our result proves the special case for caterpillars of a 1990 conjecture by Nýdl about trees.