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Trees with at least $6\ell+11$ vertices are $\ell$-reconstructible

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arxiv 2307.10035 v1 pith:OKAVVDM5 submitted 2023-07-19 math.CO

Alexandr V. Kostochka , Mina Nahvi , Douglas B. West , Dara Zirlin This is my paper · ORCID
classification math.CO
keywords deckgraphreconstructibleverticesleastvertexdeletingdetermined
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abstract

The $(n-\ell)$-deck of an $n$-vertex graph is the multiset of (unlabeled) subgraphs obtained from it by deleting $\ell$ vertices. An $n$-vertex graph is $\ell$-reconstructible if it is determined by its $(n-\ell)$-deck, meaning that no other graph has the same deck. We prove that every tree with at least $6\ell+11$ vertices is $\ell$-reconstructible.

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