Examples of difficult Hamiltonian Cycle Problems
TSPLIB contains some instances of Hamiltonian Cycle. Haythorpe [1] proposes a set of around a thousand instances which are claimed to be &quot;structurally difficult&quot; (not necessarily large).

Haythorpe, Michael. &quot;FHCP Challenge Set: The first set of structurally difficult instances of the Hamiltonian cycle problem.&quot; arXiv preprint arXiv:1902.10352 (2019).