Enumeration of Hamiltonian cycles on a thick grid cylinder - Part II: Contractible Hamiltonian cycles

Abstract

Here, in Part II, we proceeded further with the enumeration of Hamiltonian cycles (HC's) on the grid cylinder graphs of the form Pm+1?Cn, where n is allowed to grow and m is fixed. We proposed two novel characterisations of the contractible HC's. Finally, we made a conjecture concerning the dependency of the asymptotically dominant type of HC's on the parity of m.