A note on light geometric graphs

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 Ackerman and Pinchasi (2012) [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.