Imagine the graphs are really, really big. Graph isomorphism is NP-hard. Alice gives Bob a graph. Bob can ask Alice to show the bijection (hard) or show a path

Imagine the graphs are really, really big. Graph isomorphism is NP-hard. Alice gives Bob a graph. Bob can ask Alice to show the bijection (hard) or show a path (hard) but not both. Say Alice and Bob do this 40 times. Can you see how Bob should be convinced that Alice is giving him isomorphic graphs and that she knows a path through the graph? Otherwise Alice would have failed to answer one of his questions along the way.