{
  "abstract": "For finite simple graphs $G,H$ on a common vertex set $V$, we say that $H$ is $G$-colorable if $H$ admits a proper list coloring with list assignment $L(v)=N_G(v)$ for all $v\\in V$. This notion of coloring a graph using the neighborhood of another graph on the same vertex set, which we call \\emph{graphic list coloring}, has connections to several classical topics, including systems of distinct representatives and graph factorizations. In this paper, we investigate when a necessary Hall-type condition, introduced by Hilton and Johnson in 1990, is also sufficient for $H$ to be $G$-colorable. We characterize all graphs $H$ that are $G$-colorable whenever the pair $(H,G)$ satisfies Hall's condition, answering a question raised by Johnson. We then consider the dual problem of characterizing graphs $G$ such that, whenever $(H,G)$ satisfies Hall's condition, $H$ is $G$-colorable. In this vein, we obtain complete results for several families of graphs, such as forests, complete multipartite graphs, and grid graphs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.01889",
  "author_total": 1,
  "authors": [
    {
      "name": "Parikshit Chalise"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b3s1hpf7wdpb1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.01889",
  "fulltext_url": null,
  "id": "b3s1hpf7wdpb1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.01889",
  "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": "W7207652433",
  "pdf_url": "https://arxiv.org/pdf/2609.01889",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b3s1hpf7wdpb1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:20Z",
      "native_id": "2609.01889",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.01889"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Sufficiency of Hall's Condition for Graphic List Coloring",
  "title_text": "Sufficiency of Hall's Condition for Graphic List Coloring",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:20Z",
  "url": "https://research.draconitic.com/paper/b3s1hpf7wdpb1",
  "venue": "arXiv",
  "versions": []
}