On Intersection Graphs of Segments with Prescribed Slopes

  • Jakub Černý
  • Daniel Král
  • Helena Nyklová
  • Ondřej Pangrác
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2265)


We study intersection graphs of segments with prescribed slopes in the plane. A sufficient and necessary condition on tuples of slopes in order to define the same class of graphs is presented for both the possibilities that the parallel segments can or cannot overlap. Classes of intersection graphs of segments with four slopes are fully described; in particular, we find an infinite set of quadruples of slopes which define mutually distinct classes of intersection graphs of segments with those slopes.


Distinct Classis Bold Line Geometric Object Intersection Graph Intersection Realization 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Jakub Černý
    • 1
  • Daniel Král
    • 1
  • Helena Nyklová
    • 1
  • Ondřej Pangrác
    • 1
  1. 1.Department of Applied Mathematics and Institute for Theoretical Computer Science (ITI)Charles UniversityPragueCzech Republic

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