A note on light geometric graphs

Eyal Ackerman, Jacob Fox, Rom Pinchasi
2013 Discrete Mathematics  
Let G be a geometric graph on n vertices in general position in the plane. We say that G is k-light if no edge e of G has the property that each of the two open half-planes bounded by the line through e contains more than k edges of G. We extend the previous result in [1] and with a shorter argument show that every k-light geometric graph on n vertices has at most O(n √ k) edges. This bound is best possible.
doi:10.1016/j.disc.2013.03.001 fatcat:w6dv2d5f7ra4dnyskpuxaysckq