{
  "abstract": "We prove that every sufficiently large finite planar point set contains either four collinear points or seven points with at most one non-visible pair. More generally, we show that for every fixed graph $H$ with chromatic number at most five, or with chromatic number six and a color-critical edge, the visibility graph of every sufficiently large finite planar point set with no four collinear points contains a copy of $H$. These results extend the recent breakthrough of Bonnet (2026), guaranteeing six pairwise visible points, and come within one visibility edge of the next open case of the big-line-big-clique conjecture.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.25727",
  "author_total": 5,
  "authors": [
    {
      "name": "Bhaswar B. Bhattacharya"
    },
    {
      "name": "Sandip Das"
    },
    {
      "name": "Sk Samim Islam"
    },
    {
      "name": "Aashirwad Mohapatra"
    },
    {
      "name": "Saumya Sen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9bx2tvtx4082d.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.25727",
  "fulltext_url": null,
  "id": "9bx2tvtx4082d",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.25727",
  "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",
      "cs.CG"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2607|Limits and Structures in Graph Theory"
    ]
  ],
  "openalex": "W7214118838",
  "pdf_url": "https://arxiv.org/pdf/2609.25727",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9bx2tvtx4082d.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.25727",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.25727"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Large Planar Point Sets Contain 4 Collinear Points or Almost 7-Cliques, and Related Results",
  "title_text": "Large Planar Point Sets Contain 4 Collinear Points or Almost 7-Cliques, and Related Results",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/9bx2tvtx4082d",
  "venue": "arXiv",
  "versions": []
}