{
  "abstract": "A paired dominating set of a graph $G$ is a dominating set $D$ such that $G[D]$ has a perfect matching. The minimum size of such a set is the paired domination number $\\gpr(G)$. Desormeaux and Henning conjectured that every cubic bipartite graph $G$ of order $n$ satisfies $\\gpr(G)\\le n/2$. We prove the conjecture in the sharp integer form $\\gpr(G)\\le 2\\lfloor |V(G)|/4\\rfloor$ for every finite simple cubic bipartite graph $G$. The proof combines a directed contraction along a perfect matching, switching arguments based on dominator trees, a four-symbol boundary calculus for two-edge cuts, and the Gallai--Edmonds decomposition. Equality is attained by $K_{3,3}$ when $|V(G)|\\equiv2\\pmod4$ and by the cube $Q_3$ when $|V(G)|\\equiv0\\pmod4$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.30152",
  "author_total": 2,
  "authors": [
    {
      "name": "Changhong Lu"
    },
    {
      "name": "Qi Wu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6absvmrqp88h9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.30152",
  "fulltext_url": null,
  "id": "6absvmrqp88h9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.30152",
  "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": "W7214365957",
  "pdf_url": "https://arxiv.org/pdf/2609.30152",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6absvmrqp88h9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:15Z",
      "native_id": "2609.30152",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.30152"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Paired Domination in Cubic Bipartite Graphs",
  "title_text": "Paired Domination in Cubic Bipartite Graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/6absvmrqp88h9",
  "venue": "arXiv",
  "versions": []
}