There are planar graphs almost as good as the complete graphs and as short as minimum spanning trees

  • Christos Levcopoulos
  • Andrzej Lingas
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 401)


Let S be a set of n points in the plane. For an arbitrary positive rational r, we construct a planar straight-line graph on S that approximates the complete Euclidean graph on S within the factor \((1 + \tfrac{1}{r})\tfrac{{2\pi }}{{3\cos (\tfrac{\pi }{6})}}\), and it has length bounded by 2r+1 times the length of a minimum Euclidean spanning tree on S. Given the Delaunay triangulation of S, the graph can be constructed in linear time.


Span Tree Planar Graph Linear Time Complete Graph Minimum Span Tree 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Christos Levcopoulos
    • 1
    • 2
  • Andrzej Lingas
    • 1
    • 2
  1. 1.Department of Computer and Information ScienceLinköping UniversityLinköpingSweden
  2. 2.Department of Computer Science and Numerical AnalysisLund UniversityLundSweden

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