Graphs That Admit Polyline Drawings with Few Crossing Angles
Eyal Ackerman, Radoslav Fulek, Csaba D. Tóth · SIAM Journal on Discrete Mathematics · 2012
We consider graphs that admit polyline drawings where all crossings occur at the same angle $\alpha\in (0,\frac{\pi}{2}]$. We prove that every graph on n vertices that admits such a polyline drawing with at most two bends per edge has $O(n)$ edges. This result remains true when each crossing occurs at an angle from a small set of angles. We also provide several extensions that might be of independent interest.