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Disjoint compatible geometric matchings

Published: 13 June 2011 Publication History

Abstract

We prove that for every even set of $n$ pairwise disjoint line segments in the plane in general position, 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. [ABD08]. 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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Cited By

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  • (2013)Bichromatic compatible matchingsProceedings of the twenty-ninth annual symposium on Computational geometry10.1145/2462356.2462379(267-276)Online publication date: 17-Jun-2013
  • (2012)Constrained Tri-Connected Planar Straight Line GraphsThirty Essays on Geometric Graph Theory10.1007/978-1-4614-0110-0_5(49-70)Online publication date: 29-Oct-2012

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      cover image ACM Conferences
      SoCG '11: Proceedings of the twenty-seventh annual symposium on Computational geometry
      June 2011
      532 pages
      ISBN:9781450306829
      DOI:10.1145/1998196
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      Published: 13 June 2011

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      Author Tags

      1. convex subdivision
      2. dual graph
      3. geometric graph
      4. matching

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      SoCG '11
      SoCG '11: Symposium on Computational Geometry
      June 13 - 15, 2011
      Paris, France

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      View all
      • (2013)Bichromatic compatible matchingsProceedings of the twenty-ninth annual symposium on Computational geometry10.1145/2462356.2462379(267-276)Online publication date: 17-Jun-2013
      • (2012)Constrained Tri-Connected Planar Straight Line GraphsThirty Essays on Geometric Graph Theory10.1007/978-1-4614-0110-0_5(49-70)Online publication date: 29-Oct-2012

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