Contractible Hamiltonian Cycles in Polyhedral Maps

2012/02/19 by Dipendu Maity, Maity, Dipendu, Ashish Kumar Upadhyay +1
Mathematics · #57M20 #57N05 #57Q15 #Combinatorics (math.CO) #F.2.2 #FOS: Mathematics #G.2.2 #Geometric Topology (math.GT) #acm:57M20 #acm:57N05 #acm:57Q15 #math.CO #math.GT #msc:57M20 #msc:57N05 #msc:57Q15

paper · pdf · doi:10.48550/arxiv.1202.4150

9 pages, 1 figure

arxiv created 2012/02/19 · arxiv updated 2012/02/21

Abstract

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.

Related

• Hamiltonian Cycles in Polyhedral Maps
• Contractible Hamiltonian Cycles in Triangulated Surfaces
• Simple numerical algorithm for generating Hamiltonian cycles and edge labels on planar cubic maps
• Triangulated map with minimum degree four is Hamiltonian
• A New Property of Hamilton Graphs