{
  "abstract": "We give three explicit unit-distance graphs in the plane with chromatic number 5 whose vertices lie in small disks: a graph with 773 vertices inside an open disk of radius 3/2, one with 5713 vertices inside an open disk of radius 5/4, and one with 8168 vertices inside an open disk of radius 23/20. The smallest examples previously reported for these radii have 11725, 11725 and 31171 vertices. All coordinates are exact elements of Q(sqrt3, sqrt5, sqrt11). In each case 5-chromaticity is certified by an explicit 5-colouring and a DRAT proof that no 4-colouring exists. The 773-vertex graph is vertex-critical.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.06269",
  "author_total": 1,
  "authors": [
    {
      "name": "Chandan Shukla"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3dq9vnpcqchr1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.06269",
  "fulltext_url": null,
  "id": "3dq9vnpcqchr1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.06269",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.06269",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3dq9vnpcqchr1.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:21:00Z",
      "native_id": "2611.06269",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.06269"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Small 5-chromatic unit-distance graphs in disks of radius 3/2, 5/4 and 23/20",
  "title_text": "Small 5-chromatic unit-distance graphs in disks of radius 3/2, 5/4 and 23/20",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:30Z",
  "url": "https://research.draconitic.com/paper/3dq9vnpcqchr1",
  "venue": "arXiv",
  "versions": []
}