{
  "abstract": "The Erd\\H os--Sós Conjecture was recently proved by GPT-6 Astra, using a very ingenious and surprising argument. In this note, we present a simplified version of this argument in an (arguably) more natural form. We also prove a related conjecture of Addario-Berry, Havet, Linhares Sales, Reed and Thomassé, and give a substantially simplified proof of an analogous result for eulerian digraphs, again proved by GPT-6 Astra, and announced by Mubayi and Verstraete. In addition, we determine the extremal (di)graphs for all three problems.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.15893",
  "author_total": 2,
  "authors": [
    {
      "name": "Oliver Riordan"
    },
    {
      "name": "Alex Scott"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/96kg7s32z2wbj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.15893",
  "fulltext_url": null,
  "id": "96kg7s32z2wbj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.15893",
  "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": "W7213222530",
  "pdf_url": "https://arxiv.org/pdf/2609.15893",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/96kg7s32z2wbj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2609.15893",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.15893"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A short proof of the Erd\\H os--Sós Conjecture",
  "title_text": "A short proof of the Erd\\H os--Sós Conjecture",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/96kg7s32z2wbj",
  "venue": "arXiv",
  "versions": []
}