{
  "abstract": "Let $φ$ be a proper edge-coloring of a graph $G$. An edge is called rich if all edges adjacent to it receive pairwise distinct colors. The coloring $φ$ is a rich-neighbor edge-coloring if every non-isolated edge is adjacent to a rich edge. Petruševski and Škrekovski introduced this notion as a relaxation of strong edge-coloring and conjectured that every connected subcubic graph other than $K_4$ admits a rich-neighbor $5$-edge-coloring. We establish the conjectured bound for every subcubic graph $G$ satisfying $Δ(G[V_3])\\leq 1,$ where $V_3$ is the set of vertices of degree $3$ in $G$. Equivalently, the $3$-vertices of $G$ induce a matching together with isolated vertices. This extends the result of Chen, Tan and Zhou for subcubic graphs with no adjacent $3$-vertices.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.21868",
  "author_total": 3,
  "authors": [
    {
      "name": "Jiangxu Kong"
    },
    {
      "name": "Zhuming Lin"
    },
    {
      "name": "Yan Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/25cw12gx8ksc6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.21868",
  "fulltext_url": null,
  "id": "25cw12gx8ksc6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.21868",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "1703|Graph Labeling and Dimension Problems"
    ]
  ],
  "openalex": "W7222459893",
  "pdf_url": "https://arxiv.org/pdf/2610.21868",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/25cw12gx8ksc6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2610.21868",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.21868"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Rich-neighbor 5-edge-colorings of subcubic graphs whose 3-vertices induce a matching",
  "title_text": "Rich-neighbor 5-edge-colorings of subcubic graphs whose 3-vertices induce a matching",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/25cw12gx8ksc6",
  "venue": "arXiv",
  "versions": []
}