{
  "abstract": "In 2025 Cornet, Dravec, and Torres determined the domination number $γ(J(n,3))$ of the Johnson graph for every even $n \\ge 6$, expressing it as a closed form $ϕ_n$ in terms of Fort-Hedlund covering numbers, and conjectured the same value for odd $n$. We prove this conjecture: $γ(J(n,3)) = ϕ_n$ for every odd $n \\ge 7$. A dominating set of $J(n,3)$ is the same as a lotto design $\\mathrm{LD}(n,3,3,2)$, and the lotto numbers $L(n,3,3,2)$, and hence $γ(J(n,3))$, were already determined for every $n$ by Bate (1978) and by Brouwer (1981). The contribution of this paper is therefore a new proof of the odd case, carried out within the bijective framework of Cornet, Dravec, and Torres.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.10326",
  "author_total": 2,
  "authors": [
    {
      "name": "Seung-ah Lee"
    },
    {
      "name": "Semin Oh"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7fccky1yasjhy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.10326",
  "fulltext_url": null,
  "id": "7fccky1yasjhy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.10326",
  "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": "W7164137438",
  "pdf_url": "https://arxiv.org/pdf/2606.10326",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7fccky1yasjhy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2606.10326",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.10326"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Domination in Johnson graphs J(n, 3) for odd n",
  "title_text": "Domination in Johnson graphs J(n, 3) for odd n",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:42Z",
  "url": "https://research.draconitic.com/paper/7fccky1yasjhy",
  "venue": "arXiv",
  "versions": []
}