{
  "id": "2405.15733",
  "version": "v1",
  "published": "2024-05-24T17:23:01.000Z",
  "updated": "2024-05-24T17:23:01.000Z",
  "title": "Embedding Nearly Spanning Trees",
  "authors": [
    "Bruce Reed",
    "Maya Stein"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "The Erd\\H{o}s-S\\'os Conjecture states that every graph with average degree exceeding $k-1$ contains every tree with $k$ edges as a subgraph. We prove that there are $\\delta>0$ and $k_0\\in\\mathbb N$ such that the conjecture holds for every tree $T$ with $k \\ge k_0$ edges and every graph $G$ with $|V(G)| \\le (1+\\delta)|V(T)|$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-05-24T17:23:01.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "spanning trees",
      "conjecture states",
      "conjecture holds",
      "average degree exceeding"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}