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On the Edge Crossing Properties of Euclidean Minimum Weight Laman Graphs

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Algorithms and Computation (ISAAC 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8283))

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Abstract

This paper is concerned with the crossing number of Euclidean minimum-weight Laman graphs in the plane. We first investigate the relation between the Euclidean minimum-weight Laman graph and proximity graphs, and then we show that the Euclidean minimum-weight Laman graph is quasi-planar and 6-planar. Thus the crossing number of the Euclidean minimum-weight Laman graph is linear in the number of points.

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Texas at Dallas, USA

    Sergey Bereg

  2. School of Information Technologies, University of Sydney, Australia

    Seok-Hee Hong

  3. Department of Architecture and Architectural Engineering, Kyoto University, Japan

    Naoki Katoh

  4. Department of Computer Science & Institute of Information Systems and Applications, National Tsing Hua University, Taiwan, R.O.C

    Sheung-Hung Poon

  5. Research Institute for Mathematical Sciences, Kyoto University, Japan

    Shin-ichi Tanigawa

Authors
  1. Sergey Bereg
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  2. Seok-Hee Hong
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  3. Naoki Katoh
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  4. Sheung-Hung Poon
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  5. Shin-ichi Tanigawa
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, Chinese University of Hong Kong, Shatin, 100084, Hong Kong, China

    Leizhen Cai

  2. Department of Computer Science and Engineering, Hong Kong University of Science and Technology, Clear Water Bay, 100044, Hong Kong, China

    Siu-Wing Cheng

  3. Department of Computer Science, University of Hong Kong, Porfkulam, 100084, Hong Kong, China

    Tak-Wah Lam

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© 2013 Springer-Verlag Berlin Heidelberg

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Bereg, S., Hong, SH., Katoh, N., Poon, SH., Tanigawa, Si. (2013). On the Edge Crossing Properties of Euclidean Minimum Weight Laman Graphs. In: Cai, L., Cheng, SW., Lam, TW. (eds) Algorithms and Computation. ISAAC 2013. Lecture Notes in Computer Science, vol 8283. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45030-3_4

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  • DOI: https://doi.org/10.1007/978-3-642-45030-3_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-45029-7

  • Online ISBN: 978-3-642-45030-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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