Contractible Hamiltonian Cycles in Polyhedral Maps
  We present a necessary and sufficient condition for existence of a contractible Hamiltonian Cycle in the edge graph of equivelar maps on surfaces. We also present an algorithm to construct such cycles. This is further generalized and shown to hold for more general maps. 
Dipendu Maity and Ashish Kumar Upadhyay
math.CO math.GT