Hamiltonian cycles in circulant graphs and digraphs

We will discuss the status of the search for hamiltonian cycles in circulant graphs and circulant digraphs. Circulant graphs have many hamiltonian cycles, but recent joint work with Joy Morris and David Moulton uncovered a nontrivial parity condition that restricts the hamiltonian cycles in certain cases. A different parity condition arose in joint work with Stephen Locke that constructed infinitely many circulant digraphs with no hamiltonian cycles. The case of digraphs remains largely open