Drawing Planar 3-Trees with Given Face-Areas
- Cite this paper as:
- Biedl T., Ruiz Velázquez L.E. (2010) Drawing Planar 3-Trees with Given Face-Areas. In: Eppstein D., Gansner E.R. (eds) Graph Drawing. GD 2009. Lecture Notes in Computer Science, vol 5849. Springer, Berlin, Heidelberg
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.