A note on light geometric graphs

Eyal Ackerman, Jacob Fox, Rom Pinchasi

Research output: Contribution to journalArticlepeer-review


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(nk) edges. This bound is best possible.

Original languageEnglish
Pages (from-to)1281-1283
Number of pages3
JournalDiscrete Mathematics
Issue number12
StatePublished - 2013

Bibliographical note

Funding 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


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