{
  "abstract": "A strong edge colouring of a graph $G$ is an edge colouring in which every colour class is an induced matching. The minimum number of colours is the strong chromatic index $χ'_s(G)$. If each edge $e$ is assigned a list $L'(e)$ and its colour must belong to $L'(e)$, the corresponding parameter is the strong list chromatic index $χ'_{s,\\ell}(G)$. From the definitions, $χ'_s(G)\\leχ'_{s,\\ell}(G)$. Barrett et al. gave an $8$-approximation for strong edge colouring on unit disk graphs and Grelier et al. improved the approximation factor to $6$. Our first result extends this factor-$6$ guarantee from unit disk graphs to the strictly larger class of disk graphs. In another direction, Erdős and Nešetřil conjectured that the strong chromatic index of a graph of maximum degree $Δ$ is asymptotically at most $1.25Δ^2$. The best published general asymptotic upper bound has leading coefficient $1.772$, due to Hurley et al. For unit disk graphs, Dębski et al. proved that $χ'_s(G) \\leq 1.625 Δ^2$. Our second result improves this leading coefficient to $225/142 \\approx 1.5845$. In fact, the proof establishes a stronger bound $χ'_{s,\\ell}(G)\\le\\frac{225}{142} Δ^2+O(Δ)$ for unit disk graphs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.34023",
  "author_total": 5,
  "authors": [
    {
      "name": "Sandip Das"
    },
    {
      "name": "Sk Samim Islam"
    },
    {
      "name": "Aashirwad Mohapatra"
    },
    {
      "name": "Sangita Saha"
    },
    {
      "name": "Saumya Sen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/731xnkm4s705a.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.34023",
  "fulltext_url": null,
  "id": "731xnkm4s705a",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.34023",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.DM"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "1703|Graph Labeling and Dimension Problems"
    ]
  ],
  "openalex": "W7214710026",
  "pdf_url": "https://arxiv.org/pdf/2609.34023",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/731xnkm4s705a.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.34023",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.34023"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Strong Edge Colouring of Disk Graphs: A 6-Approximation and an Improved Unit-Disk Bound",
  "title_text": "Strong Edge Colouring of Disk Graphs: A 6-Approximation and an Improved Unit-Disk Bound",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/731xnkm4s705a",
  "venue": "arXiv",
  "versions": []
}