{
  "abstract": "A graph $G$ is $k$-choosable if it has a proper coloring for every $k$-list assignment. While every $C_3$-free planar graph is $4$-choosable, some of them are not $3$-choosable, as constructed by Voigt. Hu and Zhu conjectured that if $G$ is a $C_3$-free planar graph and $X \\subseteq V(G)$ induces a bipartite subgraph, then $G$ has a proper $L$-coloring whenever $|L(x)| = 3$ for $x \\in X$ and $|L(v)| = 4$ for $v \\in V(G) \\setminus X$. As evidence, they proved the conjecture when $X$ is an independent set. We provide further evidence by proving the conjecture when the induced subgraph $G[X]$ is an induced sparse matching. This is the first result supporting the conjecture in which the set $X$ receiving smaller lists may induce a subgraph with edges.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.00280",
  "author_total": 6,
  "authors": [
    {
      "name": "Stephen G. Hartke"
    },
    {
      "name": "Yupei Li"
    },
    {
      "name": "Joseph Pappe"
    },
    {
      "name": "Fares Soufan"
    },
    {
      "name": "Lin Tian"
    },
    {
      "name": "Zimu Xiang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/31t7mdq8apeg8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.00280",
  "fulltext_url": null,
  "id": "31t7mdq8apeg8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.00280",
  "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": "W7206208061",
  "pdf_url": "https://arxiv.org/pdf/2609.00280",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/31t7mdq8apeg8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:04Z",
      "native_id": "2609.00280",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.00280"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "List coloring $C_3$-free planar graphs with a sparse matching of restricted lists",
  "title_text": "List coloring C_3-free planar graphs with a sparse matching of restricted lists",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:04Z",
  "url": "https://research.draconitic.com/paper/31t7mdq8apeg8",
  "venue": "arXiv",
  "versions": []
}