The FLS zero knowledge protocol for graph hamiltonicity proceeds as follows.
The prover (proving graph hamiltonicity of graph G) picks a random cycle graph C, and sends its commitment to verifier.
Verifier picks a random bit b and sends it to sender.
If b = 0, then prover decommits all the edges of graph, and verifier verifies if its a cycle graph.
If b = 1, then prover computes isomporphism between hamiltonian cycle of G and cycle graph C. It then decommits all the edges in C that are not present in the isomporphism of G.
This protocol is proven to be honest-verifier zero knowledge in many places. How can a dishonest verifier break ZK property of this scheme? A dishonest verifier can break ZK property only if he can compute bit b depending on commitment(C) and learn some info. But that would violate hiding property of commitment scheme right?