{
  "abstract": "Chromatic choosability is a fundamental notion in list coloring. A graph $G$ is chromatic-choosable if its chromatic number $χ(G)$ equals its list chromatic number $χ_{\\ell}(G)$. In 1990, Kostochka and Sidorenko introduced the list color function of a graph $G$, denoted by $P_{\\ell}(G,m)$, which is the list-coloring analogue of its chromatic polynomial $P(G,m)$. A graph $G$ is enumeratively chromatic-choosable if $P_{\\ell}(G,m)=P(G,m)$ for every $m \\in \\mathbb{N}$. In 2002, Ohba proved that for every graph $G$, there exists an $N \\in \\mathbb{N}$ such that $K_p \\vee G$ is chromatic-choosable whenever $p \\geq N$. Allred and Mudrock recently conjectured that an analogous statement holds for enumerative chromatic choosability. In this paper, we prove that $K_1 \\vee G$ is enumeratively chromatic-choosable whenever $G$ is a theta graph. Our proof combines classical inequalities, the polynomial method, and ideas from DP (or correspondence) coloring.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.15132",
  "author_total": 10,
  "authors": [
    {
      "name": "Kingston Barnes"
    },
    {
      "name": "Vincent Fesenmeier"
    },
    {
      "name": "Braxton Gaither"
    },
    {
      "name": "Michael Guthrie"
    },
    {
      "name": "Leonardo Marciaga"
    },
    {
      "name": "Lucas Miller"
    },
    {
      "name": "Fennec Morrissette"
    },
    {
      "name": "Jeffrey A. Mudrock"
    },
    {
      "name": "Gavin Nguyen"
    },
    {
      "name": "Rose Zellner"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/eggdgeqz9fsk7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.15132",
  "fulltext_url": null,
  "id": "eggdgeqz9fsk7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.15132",
  "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": "W7221776330",
  "pdf_url": "https://arxiv.org/pdf/2610.15132",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/eggdgeqz9fsk7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.15132",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.15132"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Cones of Theta Graphs are Enumeratively Chromatic-Choosable",
  "title_text": "Cones of Theta Graphs are Enumeratively Chromatic-Choosable",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/eggdgeqz9fsk7",
  "venue": "arXiv",
  "versions": []
}