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(nk) edges. This bound is best possible.
Bibliographical noteFunding Information:
The second author’s research was supported by a Simons Fellowship, NSF grant DMS-1069197 , and by an MIT NEC Corporation Award. The third author was supported by the ISF grant (grant No. 1357/12 ) and by the BSF grant (grant No. 2008290 ).
- Geometric graphs k-near bipartite
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics