Depth of segments and circles through points enclosing many points: a note
| dc.creator | Ramos, Pedro | |
| dc.creator | Viaña, Raquel | |
| dc.date | 2008-03-07 | |
| dc.date.accessioned | 2026-07-07T09:25:39Z | |
| dc.date.available | 2026-07-07T09:25:39Z | |
| dc.description | Neumann-Lara and Urrutia showed in 1985 that in any set of n points in the plane in general positionthere is always a pair of points such that any circle through them contains at least (n-2)/60 points. In a series of papers, this result was subsequently improved till n/4.7, 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 n/4.7 points. | |
| dc.description | 5 pages, 2 figures | |
| dc.identifier | https://arxiv.org/abs/0803.1088 | |
| dc.identifier | http://arxiv.org/abs/0803.1088 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/156476 | |
| dc.subject | Combinatorics | |
| dc.subject | 52C35 | |
| dc.title | Depth of segments and circles through points enclosing many points: a note | |
| dc.type | text |