{
  "abstract": "The Erd\\H os--Sós conjecture states that every $n$-vertex graph $G$ with more than $(k-2)n/2$ edges contains every $k$-vertex tree. We solve the extremal cases of this conjecture, showing that for some fixed $μ>0$, the conjecture holds for each $G$ that minimally satisfies the assumptions of the conjecture and has a subgraph~$H$ of minimum degree $δ(H)\\ge (1-μ)k$. In our proof, we mainly have to deal with $H$ taking two different shapes: either $H$ is close to the complete graph $K_k$ or $H$ is close to the complete bipartite graph $K_{k,k}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.05411",
  "author_total": 2,
  "authors": [
    {
      "name": "Bruce Reed"
    },
    {
      "name": "Maya Stein"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9kxe4588pxf0d.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.05411",
  "fulltext_url": null,
  "id": "9kxe4588pxf0d",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.05411",
  "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": "W7211869293",
  "pdf_url": "https://arxiv.org/pdf/2609.05411",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9kxe4588pxf0d.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.05411",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.05411"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "The extremal cases of the Erd\\H os--Sós conjecture",
  "title_text": "The extremal cases of the Erd\\H os--Sós conjecture",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/9kxe4588pxf0d",
  "venue": "arXiv",
  "versions": []
}