{
  "abstract": "The Erd\\H os--Sós conjecture states that every $n$-vertex graph with more than $(k-2)n/2$ edges contains every $k$-vertex tree. We prove that for every $γ$ there is an $n_0$ such that for all $n\\ge n_0$ and $k \\ge γn$ the conjecture holds. As a corollary of our result, we obtain a solution of a 51-year-old problem of Erd\\H os and Graham on the multicolor Ramsey numbers of trees.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.05417",
  "author_total": 2,
  "authors": [
    {
      "name": "Bruce Reed"
    },
    {
      "name": "Maya Stein"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/046dj62emr1cn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.05417",
  "fulltext_url": null,
  "id": "046dj62emr1cn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.05417",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2607|Limits and Structures in Graph Theory"
    ]
  ],
  "openalex": "W7211875273",
  "pdf_url": "https://arxiv.org/pdf/2609.05417",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/046dj62emr1cn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.05417",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.05417"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "The Erd\\H os-Sós conjecture in dense graphs",
  "title_text": "The Erd\\H os-Sós conjecture in dense graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/046dj62emr1cn",
  "venue": "arXiv",
  "versions": []
}