  We revisit results obtained in [F. Harary, U. Peled, Hamiltonian threshold
graphs, Discrete Appl.~Math., 16 (1987), 11--15], where several necessary and
necessary and sufficient conditions for a connected threshold graph to be
Hamiltonian were obtained. We present these results in new forms, now stated in
terms of structural parameters that uniquely define the threshold graph and we
extend them to chain graphs. We also identify the chain graph with minimum
number of Hamilton cycles within the class of Hamiltonian chain graphs of a
given order.
