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Crossing Numbers and Stress of Random Graphs

  • Markus ChimaniEmail author
  • Hanna Döring
  • Matthias Reitzner
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11282)

Abstract

Consider a random geometric graph over a random point process in Open image in new window . Two points are connected by an edge if and only if their distance is bounded by a prescribed distance parameter. We show that projecting the graph onto a two dimensional plane is expected to yield a constant-factor crossing number (and rectilinear crossing number) approximation. We also show that the crossing number is positively correlated to the stress of the graph’s projection.

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Copyright information

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Authors and Affiliations

  1. 1.Theoretical CS, Institute of Computer ScienceUni OsnabrückOsnabrückGermany
  2. 2.Stochastics, Institute of MathematicsUni OsnabrückOsnabrückGermany

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