{
  "abstract": "We prove that every linear hypergraph on $N$ vertices with edge sizes $O(\\sqrt N)$ and $O(N^2\\log N)$ triples contained in its edges has a subset of size $Ω(\\sqrt N)$ meeting each edge in at most two vertices. As an application, every set of $N$ planar points with at most $\\sqrt N$ collinear points contains $Ω(\\sqrt N)$ points in general position. This proves a conjecture of Payne and Wood and gives the optimal quadratic bound for a geometric Ramsey problem posed by Gowers.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.34254",
  "author_total": 3,
  "authors": [
    {
      "name": "Thang Pham"
    },
    {
      "name": "Le Quang-Ham"
    },
    {
      "name": "Boqing Xue"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/58k8a94daspy4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.34254",
  "fulltext_url": null,
  "id": "58k8a94daspy4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.34254",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2607|Limits and Structures in Graph Theory"
    ]
  ],
  "openalex": "W7223954023",
  "pdf_url": "https://arxiv.org/pdf/2610.34254",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/58k8a94daspy4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.34254",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.34254"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "General-position sets and linear hypergraphs",
  "title_text": "General-position sets and linear hypergraphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/58k8a94daspy4",
  "venue": "arXiv",
  "versions": []
}