{
  "abstract": "A proper coloring $φ$ of a graph $G$ is called proper conflict-free if, for every non-isolated vertex $v$, some color appears exactly once in its open neighborhood $N_G(v)$. For a nonnegative integer $k$, a graph $G$ is proper conflict-free $(\\mathrm{degree}+k)$-choosable if, for every list assignment $L$ satisfying $|L(v)|\\ge d_G(v)+k$ for each $v\\in V(G)$, there exists a proper conflict-free coloring $φ$ of $G$ with $φ(v)\\in L(v)$ for each $v\\in V(G)$. We prove that every connected graph other than the $5$-cycle $C_5$ with maximum average degree less than $8/3$ is proper conflict-free $(\\mathrm{degree}+2)$-choosable. This improves the maximum average degree bound $18/7$ of Kashima, Škrekovski and Xu, and removes the assumption $g(G)\\ge7$ from the $8/3$ theorem of Qi, Song and Cao. As an immediate consequence, our theorem also yields that every planar graph of girth at least $8$ is proper conflict-free $(\\mathrm{degree}+2)$-choosable.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.41668",
  "author_total": 1,
  "authors": [
    {
      "name": "Huijuan Xu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dkzc7hd0qw6d0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.41668",
  "fulltext_url": null,
  "id": "dkzc7hd0qw6d0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.41668",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2610.41668",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dkzc7hd0qw6d0.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:20Z",
      "native_id": "2610.41668",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.41668"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Proper conflict-free degree-choosability of graphs with maximum average degree less than $8/3$",
  "title_text": "Proper conflict-free degree-choosability of graphs with maximum average degree less than 8/3",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:28Z",
  "url": "https://research.draconitic.com/paper/dkzc7hd0qw6d0",
  "venue": "arXiv",
  "versions": []
}