A note on light geometric graphs
Author(s)Ackerman, Eyal; Fox, Jacob; Pinchasi, Rom
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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)  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.
DepartmentMassachusetts Institute of Technology. Department of Mathematics
Ackerman, Eyal, Jacob Fox, and Rom Pinchasi. “A Note on Light Geometric Graphs.” Discrete Mathematics 313, no. 12 (June 2013): 1281–1283.
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