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Convex Polygon Intersection Graphs

  • Erik Jan van Leeuwen
  • Jan van Leeuwen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6502)

Abstract

Geometric intersection graphs are graphs determined by intersections of geometric objects. We study the complexity of visualizing the arrangements of objects that induce such graphs. We give a general framework for describing geometric intersection graphs, using arbitrary finite base sets of rationally given convex polygons and affine transformations. We prove that for every class of intersection graphs that fits the framework, the graphs in the class have a representation using polynomially many bits. Consequently, the recognition problem of these classes is in NP (and thus NP-complete). We also give an algorithm to find a drawing of the objects in the plane, if a graph class fits the framework.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Erik Jan van Leeuwen
    • 1
  • Jan van Leeuwen
    • 2
  1. 1.Department of InformaticsUniversity of BergenBergenNorway
  2. 2.Department of Information and Computing SciencesUtrecht UniversityUtrechtThe Netherlands

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