# Computing Complete Graph Isomorphisms and Hamiltonian Cycles from Partial Ones

```@article{Groe2001ComputingCG,
title={Computing Complete Graph Isomorphisms and Hamiltonian Cycles from Partial Ones},
author={A. Gro{\ss}e and J. Rothe and G. Wechsung},
journal={Theory of Computing Systems},
year={2001},
volume={35},
pages={81-93}
}```
• Published 2001
• Computer Science, Mathematics
• Theory of Computing Systems
• 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.