Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
A combinatorial result on points and circles on the plane
Discrete Mathematics
Some extremal results on circles containing points
Discrete & Computational Geometry
A combinatorial result about points and balls in Euclidean space
Discrete & Computational Geometry
A note on the circle containment problem
Discrete & Computational Geometry
Applications of random sampling in computational geometry, II
Discrete & Computational Geometry - Selected papers from the fourth ACM symposium on computational geometry, Univ. of Illinois, Urbana-Champaign, June 6 8, 1988
Open Problems in Computational Geometry
LATIN '02 Proceedings of the 5th Latin American Symposium on Theoretical Informatics
On k-Nearest Neighbor Voronoi Diagrams in the Plane
IEEE Transactions on Computers
| Hi-index | 0.00 |
Neumann-Lara and Urrutia showed in 1985 that in any set of n points in the plane in general position there is always a pair of points such that any circle through them contains at least n-260 points. In a series of papers, this result was subsequently improved till n4.7, which is currently the best known lower bound. In this paper we propose a new approach to the problem that allows us, by using known results about j-facets of sets of points in R^3, to give a simple proof of a somehow stronger result: there is always a pair of points such that any circle through them has, both inside and outside, at least n4.7 points.