There are (at least) three graphs associated with Horton, illustrated above. The first is a graph on 32 nodes. The second is a graph on 96 nodes providing a counterexample to the Tutte conjecture that every 3-regular 3-connected bipartite graph is Hamiltonian (left figure above). The third is a smaller counterexample on 92 nodes (right figure above). (A number of even smaller counterexamples have subsequently been found.)
These graphs are implemented in the Wolfram Language as GraphData["HortonGraph32"], GraphData["HortonGraph96"] and GraphData["HortonGraph92"], respectively.
The 96-node graph is constructed using a clever combination of three copies of the 32-node graph, where the 32-node graph consists of two copies of the Möbius-Kantor graph with two edges excised from each and reconnected to vertives in the other copy (Bondy and Murty 1976, pp. 61-62).
The 32-, 92- and 96-Horeon graphs have graph crossing numbers 8, 24, and 25, respectively (E. Weisstein, Oct. 20 and 25, 2025).
