Hamiltonian cycles in bipartite quadrangulations on the torus
Atsuhiro Nakamoto, Kenta Ozeki · Journal of Graph Theory · 2011
Abstract 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