Department of
Applied
Mathematics

Hamiltonicity of Cayley, vertex-transitive and certain graph covers

Guillermo Pineda Villavicencio

University of Ballarat, Australia

Abstract

We survey some of the new developments in the quest for hamiltonian cycles in Cayley and vertex transitive graphs. We consider the same problem for graphs derived from voltage graphs, called lifts. The voltage graph operation is a restricted type of a graph covering. We present conditions assuring hamiltonicity in the lift.

Finally, we finish by discussing open problems involving the notion of hamiltonicty, and some possible approaches.