{
  "abstract": "For a finite simple graph $G$ with at least one edge, the bondage number $b(G)$ is the least number of edges whose deletion increases the domination number $γ(G)$. Teschner conjectured that $b(G)\\le \\tfrac32Δ(G)$ for every graph $G$. We disprove this conjecture by giving a connected cubic bipartite graph on eighteen vertices with \\[ γ(G)=6 \\qquad\\text{and}\\qquad b(G)=5. \\] The domination number is established by a complete counting argument across the bipartition. An explicit five-edge deletion raises the domination number from six to seven. For the matching lower bound, we give an exact finite certificate: the graph has 297 minimum dominating sets, and deleting any one of its $\\binom{27}{4}=17{,}550$ four-edge subsets leaves at least one of those sets dominating. The enumeration is deterministic, uses only exact integer and set operations, and is reproduced by the complete standard-library verifier included in the appendix.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.04257",
  "author_total": 1,
  "authors": [
    {
      "name": "Yousof Yavari"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7n318vf89jahd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.04257",
  "fulltext_url": null,
  "id": "7n318vf89jahd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.04257",
  "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",
      "cs.DM"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "1703|Advanced Graph Theory Research"
    ]
  ],
  "openalex": "W7202115727",
  "pdf_url": "https://arxiv.org/pdf/2609.04257",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7n318vf89jahd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:18Z",
      "native_id": "2609.04257",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.04257"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A Counterexample to Teschner's Bondage-Number Conjecture",
  "title_text": "A Counterexample to Teschner's Bondage-Number Conjecture",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:18Z",
  "url": "https://research.draconitic.com/paper/7n318vf89jahd",
  "venue": "arXiv",
  "versions": []
}