Geodesic
Strictly convex drawings of planar graphs
Documenta mathematica, Tome 11 (2006), pp. 369-391.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Every three-connected planar graph with $n$ vertices has a drawing on an $O(n^2) \times O(n^2)$ grid in which all faces are strictly convex polygons. These drawings are obtained by perturbing (not strictly) convex drawings on $O(n) \times O(n)$ grids. Tighter bounds are obtained when the faces have fewer sides. In the proof, we derive an explicit lower bound on the number of primitive vectors in a triangle.
Classification : 05C62, 52C05
Keywords: graph drawing, planar graphs 
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Bárány, Imre; Rote, Günter. Strictly convex drawings of planar graphs. Documenta mathematica, Tome 11 (2006), pp. 369-391. http://geodesic.mathdoc.fr/item/DOCMA_2006__11__a5/