Hamiltonian cycles in bipartite quadrangulations on the torus
In this article, we shall prove that every bipartite quadrangulation G on the torus admits a simple closed curve visiting each face and each vertex of G exactly once but crossing no edge. As an application, we conclude that the radial graph of any bipartite quadrangulation on the torus has a hamiltonian cycle. Copyright  2011 Wiley Periodicals, Inc. J Graph Theory 69:143-151, 2012
hamiltonian cycle quadrangulation torus bipartite graph