Computing Complete Graph Isomorphisms and Hamiltonian Cycles from Partial Ones

André Große, Jörg Rothe, Gerd Wechsung

Abstract: We prove that computing a single pair of vertices that are mapped onto each other by an isomorphism φ between two isomorphic graphs is as hard as computing φ itself. This result optimally improves upon a result of Gál, Halevi, Lipton, and Petrank. We establish a similar, albeit slightly weaker, result about computing complete Hamiltonian cycles of a graph from partial Hamiltonian cycles.