2013/08/30 by Dipendu Maity, A. Upadhyay, Maity, Dipendu +2
Computer Science · Mathematics · #05C45 #52B70 #52C38 #Combinatorics #Combinatorics (math.CO) #FOS: Mathematics #G.2.2 #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Geometry #Hamiltonian (control theory) #Hamiltonian system #Mathematical analysis #Mathematical physics #Mathematics #Mathematics and Applications #Physics #Pure mathematics #Topological and Geometric Data Analysis #Torus #acm:05C45 #acm:52B70 #acm:52C38 #math.CO #math.GT #msc:05C45 #msc:52B70 #msc:52C38
paper · pdf · doi:10.48550/arxiv.1308.6717
18 pages
arxiv created 2013/08/30 · openalex publication_date 2013/08/30 · arxiv updated 2013/09/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
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 \citegrunbaum and Nash-Williams \citenash williams that every 4-connected graph on the torus is Hamiltonian.