Teschner's Bondage-Number Conjecture

Reproduced in full here on 13 August 2026. The counterexample is a single 18-vertex graph, so the claim is finite and was checked exhaustively rather than sampled. The edge list was transcribed from equation (3.1) and every quantity recomputed independently, without reading or running the author's verifier. Confirmed: connected, cubic and bipartite with the stated parts, 18 vertices and 27 distinct edges, so $\Delta(G) = 3$; domination number 6 by exhaustive search; and exactly 297 minimum dominating sets, the count the paper states, arrived at here independently. For the lower bound, all 20,853 edge subsets of size at most four were tested by the bundle criterion, and every one leaves at least one minimum dominating set intact, so $b(G) \ge 5$. For the upper bound, deleting the five edges 0-6, 0-10, 0-16, 1-8 and 1-11 raises the domination number to 7, recomputed from scratch on the reduced graph rather than inferred from the criterion, so $b(G) \le 5$. Therefore $b(G) = 5 > 4.5 = \frac32\Delta(G)$ and the conjecture is false. That enumeration is the entire mathematical content of the claim, so this is a complete independent check. Caveats: the preprint is two days old, is hosted on figshare rather than arXiv, and has no peer review; the acknowledgements name Eric Hou (UBC) as an independent verifier, but that is a private check, not a public endorsement by a specialist.