{
  "abstract": "Let $G$ be a graph. Under an \\emph{injective edge coloring} of $G$, any two edges at distance $2$ or belonging to a common triangle receive distinct colors. The \\emph{injective chromatic index} of $G$, denoted by $χ'_{inj}(G)$, is the smallest integer $k$ such that $G$ admits an injective edge coloring with $k$ colors. Let $Δ$ be the maximum degree of $G$. Ferdjallah et al.~proved that $χ'_{inj}(G) \\le 2(Δ-1)^2$. In this paper, we improve this bound by proving that $χ'_{inj}(G) \\le 2(Δ- 1)^2 -Δ+ 3$ if $Δ\\ge 4$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.04891",
  "author_total": 2,
  "authors": [
    {
      "name": "Lin Tian"
    },
    {
      "name": "Runze Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ey6vgkstacean.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.04891",
  "fulltext_url": null,
  "id": "ey6vgkstacean",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.04891",
  "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": "W7220716599",
  "pdf_url": "https://arxiv.org/pdf/2610.04891",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ey6vgkstacean.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.04891",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.04891"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A note on the injective edge coloring of graphs with bounded maximum degree",
  "title_text": "A note on the injective edge coloring of graphs with bounded maximum degree",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/ey6vgkstacean",
  "venue": "arXiv",
  "versions": []
}