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Wedges in Euclidean Arrangements

  • Jonathan Lenchner
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3742)

Abstract

Given an arrangement of n not all coincident lines in the Euclidean plane we show that there can be no more than \(\lfloor 4n/3\rfloor\) wedges (i.e. two-edged faces) and give explicit examples to show that this bound is tight. We describe the connection this problem has to the problem of obtaining lower bounds on the number of ordinary points in arrangements of not all coincident, not all parallel lines, and show that there must be at least \(\lfloor(5{\it n} + 6)/39\rfloor\) such points.

Keywords

Convex Hull Intersection Point Extreme Point Parallel Line Euclidean Plane 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Jonathan Lenchner
    • 1
  1. 1.IBM T.J. Watson Research InstituteYorktown Heights

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