Abstract
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 ( n k ) edges. This bound is best possible.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.