Geodesic
Strictly convex drawings of planar graphs
Documenta mathematica, Tome 11 (2006), pp. 369-391
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Every three-connected planar graph with n vertices has a drawing on an O(n2)×O(n2) grid in which all faces are strictly convex polygons. These drawings are obtained by perturbing (not strictly) convex drawings on O(n)×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.
DOI : 10.4171/dm/214
Classification : 05C62, 52C05
Mots-clés : graph drawing, planar graphs 
@article{10_4171_dm_214,
     author = {Imre B\'ar\'any and G\"unter Rote},
     title = {Strictly convex drawings of planar graphs},
     journal = {Documenta mathematica},
     pages = {369--391},
     year = {2006},
     volume = {11},
     doi = {10.4171/dm/214},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/214/}
}
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Imre Bárány; Günter Rote. Strictly convex drawings of planar graphs. Documenta mathematica, Tome 11 (2006), pp. 369-391. doi: 10.4171/dm/214

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