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arXiv · 2112.01094

Optimally reconstructing caterpillars

Zach Hunter
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Abstract

For a graph $G$, the $\ell$-deck of $G$ is the multiset of induced subgraphs on $G$ having $\ell$ vertices. Recently, Groenland et al. proved that any tree can be reconstructed from its $(8/9+o(1))n$-deck. For the particular case of caterpillar graphs, we show that the $(1/2+o(1))n$-deck suffices, which is asymptotically tight.

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Zach Hunter. 2021-12-06. Optimally reconstructing caterpillars. https://arxiv.org/abs/2112.01094

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