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Hamiltonian cycles in bipartite quadrangulations on the torus
Author(s) -
Nakamoto Atsuhiro,
Ozeki Kenta
Publication year - 2012
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.20569
Subject(s) - torus , bipartite graph , mathematics , combinatorics , hamiltonian path , vertex (graph theory) , hamiltonian (control theory) , graph , discrete mathematics , geometry , mathematical optimization
In this article, we shall prove that every bipartite quadrangulation G on the torus admits a simple closed curve visiting each face and each vertex of G exactly once but crossing no edge. As an application, we conclude that the radial graph of any bipartite quadrangulation on the torus has a hamiltonian cycle. Copyright © 2011 Wiley Periodicals, Inc. J Graph Theory 69:143‐151, 2012