{
  "abstract": "A proper coloring of the edges of a graph is one in which every $K_{1,2}$ is totally multicolored. A B-coloring is a coloring of the edges of $G$ in which every $K_{1,2}$ and every $K_{2,2}$ is totally multicolored. In this paper, we improve two results by the authors and Gyárfás. The first shows that an outerplanar graph with maximum degree $Δ$ can be B-colored with $\\max\\{Δ,9\\}$ colors, improving a bound of $Δ+1$ and this is best possible up to the constant 9. The second shows that a planar graph with maximum degree $Δ$ can be B-colored with $\\max\\{2Δ+4,22\\}$, improving a bound of $2Δ+8$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: Discrete Math. 350 (2027), no. 2, Article No. 115426",
  "arxiv": "2610.37497",
  "author_total": 3,
  "authors": [
    {
      "name": "Ryan R. Martin"
    },
    {
      "name": "Miklós Ruszinkó"
    },
    {
      "name": "Gábor N. Sárközy"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/536rtzqyj0vfe.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.37497",
  "fulltext_url": null,
  "id": "536rtzqyj0vfe",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.37497",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2610.37497",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/536rtzqyj0vfe.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.37497",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.37497"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Bounds for B-coloring planar and outerplanar graphs",
  "title_text": "Bounds for B-coloring planar and outerplanar graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/536rtzqyj0vfe",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1016/j.disc.2026.115426",
      "pid": "ck7that8ct5rk",
      "relation": "published-as",
      "title": "Bounds for B-coloring planar and outerplanar graphs",
      "venue": "Discrete Mathematics"
    }
  ]
}