Hamiltonian Cycles in Polyhedral Maps
  We present a necessary and sufficient condition for existence of a contractible, non-separating and noncontractible separating Hamiltonian cycle in the edge graph of polyhedral maps on surfaces. In particular, we show the existence of contractible Hamiltonian cycle in equivelar triangulated maps. We also present an algorithm to construct such cycles whenever it exists. 
Dipendu Maity and Ashish Kumar Upadhyay
math.CO math.GT