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arXiv · 2312.17026

On the class reconstruction number of trees

Ilia Krasikov·Yehuda Roditty·Bhalchandra D. Thatte
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Abstract

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 $T-v$.

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Ilia Krasikov, Yehuda Roditty, Bhalchandra D. Thatte. 2023-12-28. On the class reconstruction number of trees. https://arxiv.org/abs/2312.17026

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