{
  "abstract": "We prove Wang's planar D-coloring conjecture. A D-coloring of a graph is a proper edge coloring in which every subgraph isomorphic to $K_4$ minus an edge is rainbow. Wang conjectured that every planar graph of maximum degree $Δ$ has a D-coloring with 9 colors if $Δ=4$, 10 colors if $Δ=5$, and $2Δ-1$ colors if $Δ\\ge 6$. Hu, Kong and Wang proved the cases $Δ\\le 5$ and $Δ\\ge 33$. We prove the sharp bound $2Δ-1$ for every $Δ\\ge 6$, settling the remaining cases. The proof uses discharging; the case $Δ=6$ is computer-assisted.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.33322",
  "author_total": 1,
  "authors": [
    {
      "name": "Harshit Verma"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6rzpq61s25vpr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.33322",
  "fulltext_url": null,
  "id": "6rzpq61s25vpr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.33322",
  "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",
      "cs.DM"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "1703|Graph Labeling and Dimension Problems"
    ]
  ],
  "openalex": "W7223992147",
  "pdf_url": "https://arxiv.org/pdf/2610.33322",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6rzpq61s25vpr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.33322",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.33322"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A proof of Wang's planar D-coloring conjecture",
  "title_text": "A proof of Wang's planar D-coloring conjecture",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:52Z",
  "url": "https://research.draconitic.com/paper/6rzpq61s25vpr",
  "venue": "arXiv",
  "versions": []
}