Hamiltonian cycles in Cayley graphs of imprimitive complex reflection groups

Generalizing a result of Conway, Sloane, and Wilkes (1989) for real reflection groups, we show the Cayley graph of an imprimitive complex reflection group with respect to standard generating reflections has a Hamiltonian cycle. This is consistent with the long-standing conjecture that for every finite group, G , and every set of generators, S , of G the undirected Cayley graph of G with respect to S has a Hamiltonian cycle.