Hamiltonian cycles and paths in Cayley graphs and digraphs - A survey

Cayley graphs arise naturally in computer science, in the study of word-hyperbolic groups and automatic groups, in change-ringing, in creating Escher-like repeating patterns in the hyperbolic plane, and in combinatorial designs. Moreover, Babai has shown that all graphs can be realized as an induced subgraph of a Cayley graph of any sufficiently large group. Since the 1984 survey of results on hamiltonian cycles and paths in Cayley graphs by Witte and Gallian, many advances have been made. In this paper we chronicle these results and include some open problems and conjectures.