{
  "id": "2307.10035",
  "version": "v1",
  "published": "2023-07-19T15:18:49.000Z",
  "updated": "2023-07-19T15:18:49.000Z",
  "title": "Trees with at least $6\\ell+11$ vertices are $\\ell$-reconstructible",
  "authors": [
    "Alexandr V. Kostochka",
    "Mina Nahvi",
    "Douglas B. West",
    "Dara Zirlin"
  ],
  "categories": [
    "math.CO"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-07-19T15:18:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "reconstructible",
      "vertex graph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}