{
  "abstract": "A proper conflict-free coloring of a graph is a proper vertex coloring in which every non-isolated vertex has a color appearing exactly once in its neighborhood. A graph $G$ is proper conflict-free $(\\mathrm{degree}+2)$-choosable if every list assignment $L$ with $|L(v)|\\ge d_G(v)+2$ for each $v\\in V(G)$ admits such a coloring from the lists. We prove that every graph with girth at least $7$ and maximum average degree less than $8/3$ is proper conflict-free $(\\mathrm{degree}+2)$-choosable. Consequently, every planar graph of girth at least $8$ has this property, improving the previously established sufficient girth bound of $9$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.11249",
  "author_total": 3,
  "authors": [
    {
      "name": "Xingqin Qi"
    },
    {
      "name": "Huimin Song"
    },
    {
      "name": "Zhulou Cao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1dgrrxpzga848.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.11249",
  "fulltext_url": null,
  "id": "1dgrrxpzga848",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.11249",
  "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": "W7212226853",
  "pdf_url": "https://arxiv.org/pdf/2609.11249",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1dgrrxpzga848.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.11249",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.11249"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Proper conflict-free choosability of sparse graphs with girth at least seven",
  "title_text": "Proper conflict-free choosability of sparse graphs with girth at least seven",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/1dgrrxpzga848",
  "venue": "arXiv",
  "versions": []
}