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N-Flips in Triangulations with Two Odd Degree Vertices

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Abstract

In this paper, we prove that any two triangulations G and \(G'\) on the sphere with exactly two odd degree vertices can be transformed into each other by two local transformations, called an N-flip and a \(P_2\)-flip, preserving the parity of degree of each vertex, if \(|V(G)|=|V(G')|\). This is an analogy of the same result for triangulations with each vertex even degree [7], but we prove such a fact does not hold for triangulations with at least four odd degree vertices.

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Authors and Affiliations

  1. Department of Mathematics, Keio University, Tokyo, Japan

    Yoshihiro Asayama

  2. Faculty of Environment and Information Sciences, Yokohama National University, Yokohama, Japan

    Ryo Matsukawa & Atsuhiro Nakamoto

  3. Research Institute for Digital Media and Content, Keio University, Tokyo, Japan

    Naoki Matsumoto

Authors
  1. Yoshihiro Asayama
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  2. Ryo Matsukawa
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  3. Naoki Matsumoto
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  4. Atsuhiro Nakamoto
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Correspondence to Naoki Matsumoto.

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Asayama, Y., Matsukawa, R., Matsumoto, N. et al. N-Flips in Triangulations with Two Odd Degree Vertices. Graphs and Combinatorics 36, 469–490 (2020). https://doi.org/10.1007/s00373-019-02130-2

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  • DOI: https://doi.org/10.1007/s00373-019-02130-2

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