Salvato in:
| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2312.17026 |
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Sommario:
- Harary and Lauri conjectured that the class reconstruction number of trees is 2, that is, each tree has two unlabelled vertex-deleted subtrees that are not both in the deck of any other tree. We show that each tree $T$ can be reconstructed up to isomorphism given two of its unlabelled subgraphs $T-u$ and $T-v$ under the assumption that $u$ and $v$ are chosen in a particular way. Our result does not completely resolve the conjecture of Harary and Lauri since the special property defining $u$ and $v$ cannot be recognised from the given subtrees $T-u$ and $T-v$.