Chapter

Algorithms and Computation

Volume 8283 of the series Lecture Notes in Computer Science pp 33-43

On the Edge Crossing Properties of Euclidean Minimum Weight Laman Graphs

  • Sergey BeregAffiliated withDepartment of Computer Science, University of Texas at Dallas
  • , Seok-Hee HongAffiliated withSchool of Information Technologies, University of Sydney
  • , Naoki KatohAffiliated withDepartment of Architecture and Architectural Engineering, Kyoto University
  • , Sheung-Hung PoonAffiliated withDepartment of Computer Science & Institute of Information Systems and Applications, National Tsing Hua University
  • , Shin-ichi TanigawaAffiliated withResearch Institute for Mathematical Sciences, Kyoto University

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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.