Hamiltonian Decomposition of the Rectangular Twisted Torus

Abstract

We show that the 2a\times a rectangular twisted torus introduced by Camara et al. [5] is edge decomposable into two Hamiltonian cycles. In the process, the 2a × a × a prismatic twisted torus is edge decomposable into three Hamiltonian cycles, and the 2a × a × a prismatic doubly twisted torus admits two edge-disjoint Hamiltonian cycles.