Cubic Planar Graphs that cannot be Drawn on few Lines

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For every integer $ell$, we construct a cubic 3-vertex-connected planar bipartite graph $G$ with $O(ell^3)$ vertices such that there is no planar straight-line drawing of $G$ whose vertices all lie on $ell$ lines. This strengthens previous results on graphs that cannot be drawn on few lines, which constructed significantly larger maximal ...More