Hamiltonian Cycles in Polyhedral Maps

2014/05/07 by Dipendu Maity, Maity, Dipendu, Ashish Kumar Upadhyay +1
Mathematics · #05C38 #57M20 #57N05 #Combinatorics (math.CO) #FOS: Mathematics #Geometric Topology (math.GT) #math.CO #math.GT #msc:05C38 #msc:57M20 #msc:57N05

paper · pdf · doi:10.48550/arxiv.1405.1599

14 pages

arxiv created 2014/05/07 · arxiv updated 2014/05/08

Abstract

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.

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