{
  "abstract": "A dominating set $D$ of a graph $G$ is a \\emph{fair dominating set} if every two vertices outside $D$ have the same number of neighbors in $D$, and the \\emph{fair domination number} $\\mathrm{fd}(G)$ is the minimum cardinality of such a set. Caro, Hansberg and Henning, who introduced this parameter, proved that $\\mathrm{fd}(G)<17n/19$ for every maximal outerplanar graph $G$ of order $n\\geq3$, and asked whether this bound is asymptotically best possible. We show that it is not the case by proving $\\mathrm{fd}(G)\\leq(7n-3)/8<7n/8$ for every maximal outerplanar graph $G$ of order $n\\geq3$, and we exhibit an infinite family of maximal outerplanar graphs with $\\mathrm{fd}(G)/n\\rightarrow7/9$, so that the best asymptotic constant lies between $7/9$ and $7/8$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.23076",
  "author_total": 2,
  "authors": [
    {
      "name": "Yair Caro"
    },
    {
      "name": "Riste Škrekovski"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6qd3dft2ybxhd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.23076",
  "fulltext_url": null,
  "id": "6qd3dft2ybxhd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.23076",
  "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|Advanced Graph Theory Research"
    ]
  ],
  "openalex": "W7214000351",
  "pdf_url": "https://arxiv.org/pdf/2609.23076",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6qd3dft2ybxhd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.23076",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.23076"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "An improved upper bound for the fair domination number of maximal outerplanar graphs",
  "title_text": "An improved upper bound for the fair domination number of maximal outerplanar graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/6qd3dft2ybxhd",
  "venue": "arXiv",
  "versions": []
}