On the Edge Crossing Properties of Euclidean Minimum Weight Laman Graphs

  • Sergey Bereg
  • Seok-Hee Hong
  • Naoki Katoh
  • Sheung-Hung Poon
  • Shin-ichi Tanigawa
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8283)

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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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Sergey Bereg
    • 1
  • Seok-Hee Hong
    • 2
  • Naoki Katoh
    • 3
  • Sheung-Hung Poon
    • 4
  • Shin-ichi Tanigawa
    • 5
  1. 1.Department of Computer ScienceUniversity of Texas at DallasUSA
  2. 2.School of Information TechnologiesUniversity of SydneyAustralia
  3. 3.Department of Architecture and Architectural EngineeringKyoto UniversityJapan
  4. 4.Department of Computer Science & Institute of Information Systems and ApplicationsNational Tsing Hua UniversityTaiwan, R.O.C
  5. 5.Research Institute for Mathematical SciencesKyoto UniversityJapan

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