Convex drawings of Planar Graphs and
the Order Dimension of 3-Polytopes
We define an analogue of Schnyder's tree decompositions for
3-connected planar graphs. Based on this structure we obtain:
Institut für Informatik
Freie Universität Berlin
Takustr. 9, D-14195 Berlin
Let G be a 3-connected planar graph with f faces, then G has a
convex drawing with its vertices embedded on the
Let G be a 3-connected planar graph. The dimension of the incidence order of
vertices, edges and bounded faces of G
is at most 3.
The second result is originally due to Brightwell and Trotter.
Here we give a substantially simpler proof.
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