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For every integer $\ell$, we construct a cubic 3-vertex-connected planarbipartite graph $G$ with $O(\ell^3)$ vertices such that there is no planarstraight-line drawing of $G$ whose vertices all lie on $\ell$ lines. Thisstrengthens previous results on graphs that cannot be drawn on few lines, whichconstructed significantly larger maximal planar graphs. We also find apex-treesand cubic bipartite series-parallel graphs that cannot be drawn on a boundednumber of lines.

Cubic Planar Graphs that cannot be Drawn on few Lines