#### DOCUMENTA MATHEMATICA, Vol. 11 (2006), 369-391

Imre Bárány and Günter Rote

Strictly Convex Drawings of Planar Graphs

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.

2000 Mathematics Subject Classification: Primary 05C62; Secondary 52C05.

Keywords and Phrases: Graph drawing, planar graphs.

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