Is there any problem of enumeration of discrete objects for which problem of recognizing of these discrete objects is coNP-complete (or NP-complete), but it is possible to enumerate all these objects in output polynomial time?For example (but I don't know about the complexity of enumeration) the problem of enumeration (generation) all Hamiltonian graphs with no more than n vertices.
Enumeration of discrete objects for which recognition problem is coNP-complete
cc.complexity theory;np hardness