Intersection graphs of noncrossing arc-connected sets in the plane

  • Jan Kratochvíl
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1190)

Abstract

Arc-connected sets A, BE2 are called noncrossing if both A-B and B-A are arc-connected. A graph is called an NCAC graph if it has an intersection representation in which vertices are represented by arc-connected sets in the plane and any two sets of the representation are noncrossing. In particular, disk intersection graphs are NCAC. By a unified reduction we show that recognition of disk intersection and NCAC graphs are NP-hard. A simple observation shows that triangle-free disk intersection and NCAC graphs are planar, and hence recognizable in polynomial time. On the other hand, recognition of triangle-free AC graphs (intersection graphs of arc-connected sets) is still NP-hard.

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Copyright information

© Springer-Verlag 1997

Authors and Affiliations

  • Jan Kratochvíl
    • 1
  1. 1.Department of Applied MathematicsCharles UniversityPragueCzech Republic

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