Triangle-Free Planar Graphs as Segments Intersection Graphs

  • N. de Castro
  • F. J. Cobos
  • J. C. Dana
  • A. Márquez
  • M. Noy
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1731)


We prove that every triangle-free planar graph is the graph of intersection of a set of segments in the plane. Moreover, the segments can be chosen in only three directions (horizontal, vertical and oblique) and in such a way that no two segments cross, i.e., intersect in a common interior point.


Planar Graph Intersection Graph Vertical Segment Outer Face Horizontal Segment 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • N. de Castro
    • 1
  • F. J. Cobos
    • 1
  • J. C. Dana
    • 1
  • A. Márquez
    • 1
  • M. Noy
    • 2
  1. 1.Departamento de Matemática Aplicada IUniversidad de SevillaSpain
  2. 2.Dpto. de Matemática Aplicada IIUniversitat Politècnica de CatalunyaSpain

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