Discrete & Computational Geometry

, Volume 49, Issue 1, pp 89–131 | Cite as

Disjoint Compatible Geometric Matchings

  • Mashhood Ishaque
  • Diane L. Souvaine
  • Csaba D. Tóth


We prove that for every set of n pairwise disjoint line segments in the plane in general position, where n is even, there is another set of n segments such that the 2n segments form pairwise disjoint simple polygons in the plane. This settles in the affirmative the Disjoint Compatible Matching Conjecture by Aichholzer et al. (Comput. Geom. 42:617–626, 2009). The key tool in our proof is a novel subdivision of the free space around n disjoint line segments into at most n+1 convex cells such that the dual graph of the subdivision contains two edge-disjoint spanning trees.


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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Mashhood Ishaque
    • 1
  • Diane L. Souvaine
    • 1
  • Csaba D. Tóth
    • 1
    • 2
  1. 1.Department of Computer ScienceTufts UniversityMedfordUSA
  2. 2.Department of Mathematics and StatisticsUniversity of CalgaryCalgaryCanada

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