{
  "abstract": "We prove that every claw-free perfect graph $G$ satisfies $\\ch(G)=χ(G)=ω(G)$. More strongly, if $S$ is a clique of simplicial vertices of $G$ and $k\\geω(G)$, every proper precoloring of $S$ extends to a proper coloring of $G$ from arbitrary lists of size $k$ on $V(G)\\setminus S$. The proof has three coloring steps: a mixed-list theorem for cobipartite graphs, a precoloring-extension theorem for elementary graphs built on Galvin's kernel method and a homogeneous-pair exchange argument, and a polynomial method (Combinatorial Nullstellensatz) argument for graphs of interval type in which a Vandermonde factor is transferred across each incomplete pair. The three coloring steps are assembled along the structure theorems of Chvátal--Sbihi, Maffray--Reed and Chudnovsky--Seymour, using double clique cutsets for composition. As a consequence, every perfect line graph is chromatic-choosable, recovering the theorem of Peterson and Woodall. Our precoloring extension theorem also resolves a conjecture posed by Chudnovsky and Seymour.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.01068",
  "author_total": 3,
  "authors": [
    {
      "name": "Suchismita Mishra"
    },
    {
      "name": "Narayanan Narayanan"
    },
    {
      "name": "Umesh Shankar"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4zq47w46dv3g9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.01068",
  "fulltext_url": null,
  "id": "4zq47w46dv3g9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.01068",
  "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",
      "cs.DM"
    ],
    [
      "arxiv",
      "math.CO"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.01068",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4zq47w46dv3g9.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.01068",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.01068"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Claw-free perfect graphs are chromatic-choosable",
  "title_text": "Claw-free perfect graphs are chromatic-choosable",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/4zq47w46dv3g9",
  "venue": "arXiv",
  "versions": []
}