Hamiltonian cycles in bipartite quadrangulations on the torus |
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| Authors: | Atsuhiro Nakamoto Kenta Ozeki |
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| Institution: | 1. Department of Mathematics, Yokohama National University 79‐2 Tokiwadai, Hodogaya‐ku, Yokohama 240‐8501, Japan;2. Department of Mathematics, Keio University, 3‐14‐1 Hiyoshi, Kohoku‐ku, Yokohama 223‐0061, Japan |
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| Abstract: | 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 |
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| Keywords: | Hamiltonian cycle quadrangulation bipartite graph torus |
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