{
  "abstract": "In this paper we prove that every graph $G$ with no induced six-vertex path satisfies $χ(G)\\le ω(G)^{c\\log_2ω(G)}$ for $c=45/\\log_2(4/3)<109$. The best previous bound was exponential in $ω(G)$. Our result is the first quasi-polynomial bound for $P_6$-free graphs and generalizes the bound for $P_5$-free graphs by Scott, Seymour, and Spirkl [Polynomial bounds for chromatic number. {IV}. {A} near-polynomial bound for excluding the five-vertex path. {\\em Combinatorica}, 43(5):845--852, 2023].",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.33407",
  "author_total": 3,
  "authors": [
    {
      "name": "Shenwei Huang"
    },
    {
      "name": "Yidong Zhou"
    },
    {
      "name": "Yuwen Zhou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9qpc7s3jcmrgt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.33407",
  "fulltext_url": null,
  "id": "9qpc7s3jcmrgt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.33407",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2610.33407",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9qpc7s3jcmrgt.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.33407",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.33407"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A quasi-polynomial $χ$-bound for $P_6$-free graphs",
  "title_text": "A quasi-polynomial χ-bound for P_6-free graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/9qpc7s3jcmrgt",
  "venue": "arXiv",
  "versions": []
}