Notes on Hamiltonian threshold and chain graphs

Abstract

We revisit results obtained in [1], 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.

Keywords

• threshold graph
• chain graph
• hamiltonian graph
• algorithm
• binary sequence