Let G be a geometric graph on n vertices in general position in the plane. Suppose that for every line ℓ in the plane the subgraph of G induced by the set of vertices in one of the two half-planes bounded by ℓ has at most k edges (k<1 may be a function of n). Then G has at most O(nk) edges. This bound is best possible.
Bibliographical noteFunding Information:
We thank anonymous referees for several helpful suggestions for improving the presentation of the paper. The second author was supported by BSF grant (grant No. 2008290 ).
- Geometric graphs
- k-near bipartite
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics