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The Number of Diagonal Transformations in Quadrangulations on the Sphere

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Computational Geometry and Graphs (TJJCCGG 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8296))

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Abstract

A quadrangulation is a spherical map of a simple graph such that each face is bounded by a cycle of length four. Since every quadrangulation G is bipartite, G has a unique bipartition V(G) = B ∪ W, where we call (|B|,|W|) the bipartition size of G. In this article, we shall prove that any two quadrangulations G and G′ with the same bipartition size can be transformed into each other by at most 10|B| + 16|W| − 64 diagonal slides.

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Author information

Authors and Affiliations

  1. Graduate School of Environment and Information Sciences, Yokohama National University, 79-2 Tokiwadai, Hodogaya-ku, Yokohama, 240-8501, Japan

    Naoki Matsumoto

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

    Atsuhiro Nakamoto

Authors
  1. Naoki Matsumoto
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  2. Atsuhiro Nakamoto
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Editor information

Editors and Affiliations

  1. Research Center for Math and Science Education, Tokyo University of Science, 1-3 Kagurazaki, 162-8601, Shinjuku, Tokyo, Japan

    Jin Akiyama

  2. Department of Computer and Information Science, Ibaraki University, Hitachi, Ibaraki, Japan

    Mikio Kano

  3. Research Institute of Educational Development, Tokai University, Tomigaya, Shibuya-ku, Tokyo, Japan

    Toshinori Sakai

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Matsumoto, N., Nakamoto, A. (2013). The Number of Diagonal Transformations in Quadrangulations on the Sphere. In: Akiyama, J., Kano, M., Sakai, T. (eds) Computational Geometry and Graphs. TJJCCGG 2012. Lecture Notes in Computer Science, vol 8296. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45281-9_11

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  • DOI: https://doi.org/10.1007/978-3-642-45281-9_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-45280-2

  • Online ISBN: 978-3-642-45281-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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