{
  "abstract": "In 2018, Goddard and Henning conjectured that every cubic graph has four total dominating sets covering each vertex at most twice, and asked the analogous question for transversals of $3$-uniform $3$-regular hypergraphs. We prove the conjecture, which also answers the question in the affirmative.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.19450",
  "author_total": 3,
  "authors": [
    {
      "name": "Hyemin Kwon"
    },
    {
      "name": "Boram Park"
    },
    {
      "name": "Yoshio Sano"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f4ze7453w5saa.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.19450",
  "fulltext_url": null,
  "id": "f4ze7453w5saa",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.19450",
  "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",
      "math.CO"
    ],
    [
      "openalex",
      "1703|Advanced Graph Theory Research"
    ]
  ],
  "openalex": "W7222245828",
  "pdf_url": "https://arxiv.org/pdf/2610.19450",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f4ze7453w5saa.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.19450",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.19450"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Every cubic graph has four total dominating sets covering each vertex at most twice",
  "title_text": "Every cubic graph has four total dominating sets covering each vertex at most twice",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/f4ze7453w5saa",
  "venue": "arXiv",
  "versions": []
}