ISAAC 2013: Algorithms and Computation pp 33-43

# 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.

## Keywords

Delaunay Triangulation Supporting Line Sparse Graph Longe Edge Interpoint Distance
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## 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