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Discrete & Computational Geometry

, Volume 21, Issue 3, pp 321–328 | Cite as

On the Boundary of the Union of Planar Convex Sets

  • J. Pach
  • M. Sharir

Abstract.

We give two alternative proofs leading to different generalizations of the following theorem of [1]. Given n convex sets in the plane, such that the boundaries of each pair of sets cross at most twice, then the boundary of their union consists of at most 6n-12 arcs. (An arc is a connected piece of the boundary of one of the sets.) In the generalizations we allow pairs of boundaries to cross more than twice.

Keywords

Alternative Proof Planar Convex Connected Piece 
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.

Copyright information

© Springer-Verlag New York Inc. 1999

Authors and Affiliations

  • J. Pach
    • 1
  • M. Sharir
    • 2
  1. 1.Department of Computer Science, City College, CUNY, New York, NY 10031, USA US
  2. 2.Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA pach@cims.nyu.edu US

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