{
  "abstract": "An $\\mathrm{ISK}_4$ is a graph that is isomorphic to a subdivision of $K_4$; a \\textit{diamond} is $K_4$ minus one edge; and a \\textit{bowtie} consists of two triangles sharing exactly one vertex. Lévêque, Maffray, and Trotignon~(2012) conjectured that every $\\mathrm{ISK}_4$-free graph is $4$-colorable. Chen, Chen, Cui, Feng, and Liu~(2021) proved this for $\\{\\textup{diamond},\\textup{bowtie}\\}$-free graphs. We prove this conjecture for diamond-free graphs. Moreover, the bound is optimal.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.32404",
  "author_total": 2,
  "authors": [
    {
      "name": "Qing Cui"
    },
    {
      "name": "Kaiyang Lan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/01w80fzwr1hz1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.32404",
  "fulltext_url": null,
  "id": "01w80fzwr1hz1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.32404",
  "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",
      "1703|Advanced Graph Theory Research"
    ]
  ],
  "openalex": "W7223683136",
  "pdf_url": "https://arxiv.org/pdf/2610.32404",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/01w80fzwr1hz1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:19Z",
      "native_id": "2610.32404",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.32404"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "The chromatic number of $\\{\\mathrm{ISK}_4, \\textup{diamond}\\}$-free graphs",
  "title_text": "The chromatic number of {ISK_4, textupdiamond}-free graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:19Z",
  "url": "https://research.draconitic.com/paper/01w80fzwr1hz1",
  "venue": "arXiv",
  "versions": []
}