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Diagonal Flips in Hamiltonian Triangulations on the Sphere

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Abstract.

In this paper, we shall prove that any two Hamiltonian triangulations on the sphere with n≥5 vertices can be transformed into each other by at most 4n−20 diagonal flips, preserving the existence of Hamilton cycles. Moreover, using this result, we shall prove that at most 6n−30 diagonal flips are needed for any two triangulations on the sphere with n vertices to transform into each other.

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Authors and Affiliations

  1. Department of Mathematics, Yokohama National University, 79-2 Tokiwadai, Hodogaya-ku, Yokohama, 240-8501, Japan

    Ryuichi Mori & Atsuhiro Nakamoto

  2. Department of Mathematics, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama, 223-8522, Japan

    Katsuhiro Ota

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  1. Ryuichi Mori
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  2. Atsuhiro Nakamoto
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  3. Katsuhiro Ota
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Mori, R., Nakamoto, A. & Ota, K. Diagonal Flips in Hamiltonian Triangulations on the Sphere. Graphs and Combinatorics 19, 413–418 (2003). https://doi.org/10.1007/s00373-002-0508-6

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  • DOI: https://doi.org/10.1007/s00373-002-0508-6

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