Drawing Planar 3-Trees with Given Face-Areas

  • Therese Biedl
  • Lesvia Elena Ruiz Velázquez
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5849)


We study straight-line drawings of planar graphs such that each interior face has a prescribed area. It was known that such drawings exist for all planar graphs with maximum degree 3. We show here that such drawings exist for all planar partial 3-trees, i.e., subgraphs of a triangulated planar graph obtained by repeatedly inserting a vertex in one triangle and connecting it to all vertices of the triangle. Moreover, vertices have rational coordinates if the face-areas are rational, and we can bound the resolution. We also give some negative results for other graph classes.


Planar Graph Face Area Graph Class Outerplanar Graph Interior Face 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Therese Biedl
    • 1
  • Lesvia Elena Ruiz Velázquez
    • 1
  1. 1.David R. Cheriton School of Computer ScienceUniversity of WaterlooWaterlooCanada

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