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


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.


Alternative Proof Planar Convex Connected Piece 
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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 US

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