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

TL;DR

This paper proves that all trees with at least 6ℓ+11 vertices can be uniquely reconstructed from their (n−ℓ)-deck, advancing understanding of graph reconstruction.

Contribution

It establishes a new lower bound on the size of trees that are ℓ-reconstructible, specifically trees with at least 6ℓ+11 vertices.

Findings

Trees with at least 6ℓ+11 vertices are ℓ-reconstructible

Provides a bound for reconstructibility based on tree size

Advances graph reconstruction theory for trees

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.