{
  "abstract": "For a graph $G$, a proper edge coloring of $G$ is called a D-coloring if every diamond subgraph of $G$ is rainbow. Let $χ'_D(G)$ be the D-chromatic index of $G$, which is the smallest integer $k$ such that $G$ admits a D-coloring with $k$ colors. Let $Δ$ be the maximum degree of $G$. The only known Brooks-type upper bound on $χ'_D(G)$ is $\\frac{9}{16}Δ^2 + \\frac{1}{2}Δ$, given by a greedy coloring. In this paper, using a probabilistic method, we obtain the first improvement upon this upper bound by proving that $χ'_D(G) \\le (1-c)\\frac{9}{16}Δ^2$ for some $c > 0$ and sufficiently large $Δ$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.01875",
  "author_total": 2,
  "authors": [
    {
      "name": "Lin Tian"
    },
    {
      "name": "Runze Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/16sfa58qceh1r.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.01875",
  "fulltext_url": null,
  "id": "16sfa58qceh1r",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.01875",
  "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|Graph Labeling and Dimension Problems"
    ]
  ],
  "openalex": "W7207770528",
  "pdf_url": "https://arxiv.org/pdf/2609.01875",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/16sfa58qceh1r.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:20Z",
      "native_id": "2609.01875",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.01875"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A stronger upper bound on the D-chromatic index",
  "title_text": "A stronger upper bound on the D-chromatic index",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:20Z",
  "url": "https://research.draconitic.com/paper/16sfa58qceh1r",
  "venue": "arXiv",
  "versions": []
}