Hamiltonian Cycle in Semi-Equivelar Maps on the Torus

الأصل · EN

Semi-Equivelar maps are generalizations of Archimedean solids to the surfaces other than 2-sphere. There are eight semi-equivelar maps of types {3³,4²}, {3²,4,3,4}, {6,3,6,3}, {3⁴,6}, {4,8²}, {3,12²}, {4,6,12}, {6,4,3,4} exist on the torus. In this article we show the existence of Hamiltonian cycle in each semi-equivelar map on the torus except the map of type {3,12²}. This result gives the partial solution to the conjecture which is given by Grunbaum grunbaum and Nash-Williams nash williams that every 4-connected graph on the torus is Hamiltonian.