{
  "abstract": "We prove that every finite simple maximal planar graph of maximum degree at most six admits a total eight-coloring. We first show that every proper vertex four-coloring of a subcubic graph extends to a total five-coloring. A curvature inequality for boundary walks then gives a matching decomposition of four-connected triangulations with degrees five and six, extending their prescribed vertex four-colorings to total eight-colorings. In a minimum counterexample, two local boundary colorings force the degree-four vertices to have disjoint neighborhoods. A characterization of the local extension obstructions permits these vertices to be restored simultaneously. The proof uses Hamiltonian-connectedness of four-connected planar graphs and Kardoš's Hamiltonicity theorem for three-connected cubic planar graphs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.32717",
  "author_total": 1,
  "authors": [
    {
      "name": "Enqiang Zhu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/exdvp218hpasg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.32717",
  "fulltext_url": null,
  "id": "exdvp218hpasg",
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  "landing_url": "https://arxiv.org/abs/2610.32717",
  "language": null,
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  "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"
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    [
      "openalex",
      "1703|Graph Labeling and Dimension Problems"
    ]
  ],
  "openalex": "W7223700231",
  "pdf_url": "https://arxiv.org/pdf/2610.32717",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/exdvp218hpasg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.32717",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.32717"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Total eight-colorings of maximal planar graphs of maximum degree six",
  "title_text": "Total eight-colorings of maximal planar graphs of maximum degree six",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/exdvp218hpasg",
  "venue": "arXiv",
  "versions": []
}