Strictly convex drawings of planar graphs
<|reference_start|>Strictly convex drawings of planar graphs: Every three-connected planar graph with n vertices has a drawing on an O(n^2) x 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) x O(n) grids. More generally, a strictly convex drawing exists on a grid of size O(W) x O(n^4/W), for any choice of a parameter W in the range n<W<n^2. 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.<|reference_end|>
@article{barany2005strictly,
    title={Strictly convex drawings of planar graphs},
    author={Imre Barany and Guenter Rote},
    journal={DOCUMENTA MATHEMATICA, Vol. 11 (2006), 369-391},
    year={2005},
    archivePrefix={arXiv},
    eprint={cs/0507030},
    primaryClass={cs.CG cs.DM}
}