{
  "abstract": "Let $G$ be a simple graph with maximum degree $Δ\\ge 3$, and let $P(G,k)$ denote its chromatic polynomial. For each positive integer $k$, the list-color function $P_{\\ell}(G,k)$ is the minimum number of $L$-colorings of $G$ over all $k$-assignments $L$. In this paper, we prove that $P_{\\ell}(G,k)=P(G,k)$ for every integer $k\\ge 23.41Δ$. This gives a threshold for equality that is linear in the maximum degree and independent of the number of vertices or edges. It improves the known sufficient condition $k\\ge |E(G)|-1$ for graphs with sufficiently many edges relative to their maximum degree.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.08540",
  "author_total": 2,
  "authors": [
    {
      "name": "Meiqiao Zhang"
    },
    {
      "name": "Fengming Dong"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a3190bqxf4f85.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.08540",
  "fulltext_url": null,
  "id": "a3190bqxf4f85",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.08540",
  "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": "W7212073232",
  "pdf_url": "https://arxiv.org/pdf/2609.08540",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a3190bqxf4f85.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:30Z",
      "native_id": "2609.08540",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.08540"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "When chromatic polynomials coincide with list-color functions: a threshold linear in the maximum degree",
  "title_text": "When chromatic polynomials coincide with list-color functions: a threshold linear in the maximum degree",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:30Z",
  "url": "https://research.draconitic.com/paper/a3190bqxf4f85",
  "venue": "arXiv",
  "versions": []
}