English

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

Combinatorics 2023-07-20 v1

Abstract

The (n)(n-\ell)-deck of an nn-vertex graph is the multiset of (unlabeled) subgraphs obtained from it by deleting \ell vertices. An nn-vertex graph is \ell-reconstructible if it is determined by its (n)(n-\ell)-deck, meaning that no other graph has the same deck. We prove that every tree with at least 6+116\ell+11 vertices is \ell-reconstructible.

Keywords

Cite

@article{arxiv.2307.10035,
  title  = {Trees with at least $6\ell+11$ vertices are $\ell$-reconstructible},
  author = {Alexandr V. Kostochka and Mina Nahvi and Douglas B. West and Dara Zirlin},
  journal= {arXiv preprint arXiv:2307.10035},
  year   = {2023}
}