Enumeration of Hamiltonian cycles on a thick grid cylinder - Part I: Non-contractible hamiltonian cycles

Abstract

© 2018 - Applicable Analysis and Discrete Mathematics. In a recent paper, we have studied the enumeration of Hamiltonian cycles (abbreviated HCs) on the grid cylinder graph P m+1 × C n , where m grows while n is fixed. In this sequel, we study a much harder problem of enumerating HCs on the same graph only this time letting n grow while m is fixed. We propose a characterization for non-contractible HCs which enables us to prove that their numbers h mnc (n) satisfy a recurrence relation for every fixed m. From the computational data, we conjecture that the coefficient for the dominant positive characteristic root in the explicit formula for h mnc (n) is 1.