Document
type: Class

Discrete and Computational Geometry
type: Thing
publication venue for: k-Sets, convex quadrilaterals, and the rectilinear crossing number of Kn*
type: Document
type: Journal
type: Information Content Entity
type: Generically Dependent Continuant
type: Entity
type: Continuant
type: Periodical
type: Collection

Continuant
type: Class

Entity
type: Class

Generically Dependent Continuant
type: Class

RDF description of k-Sets, convex quadrilaterals, and the rectilinear crossing number of Kn* - http://orbis.uaslp.mx/vivo/individual/scopus1641
rights: termsOfUse
date: 2026-08-27T08:17:20
publisher: vivo
type: Document

Article
type: Class

Information Content Entity
type: Class

k-Sets, convex quadrilaterals, and the rectilinear crossing number of Kn*
related by: authorship 9846
type: Generically Dependent Continuant
type: Document
has publication venue: Discrete and Computational Geometry
issue: 4
type: Article
type: Entity
abstract: We use circular sequences to give an improved lower bound on the minimum number of (≤ k)-sets in a set of points in general position. We then use this to show that if S is a set of n points in general position, then the number D(S) of convex quadrilaterals determined by the points in S is at least 0.37553(4n) O(n3). This in turn implies that the rectilineal crossing number cr̄(Kn) of the complete graph Kn is at least 0.37553 (4n) O (n n), and that Sylvester%27s Four Point Problem Constant is at least 0.37553. These improved bounds refine results recently obtained by Ábrego and Fernández-Merchant and by Lovász, Vesztergombi, Wagner, and Welzl.
e iscopus: 2-s2.0-33646490302
type: Continuant
related by: authorship 9847
crisid: 1642
page start: 671
accesstype: All Open Access, Bronze
most specific type: Article
page end: 690
most specific type: Document
abstract: We use circular sequences to give an improved lower bound on the minimum number of (≤ k)-sets in a set of points in general position. We then use this to show that if S is a set of n points in general position, then the number D(S) of convex quadrilaterals determined by the points in S is at least 0.37553(4n) %2b O(n3). This in turn implies that the rectilineal crossing number cr̄(Kn) of the complete graph Kn is at least 0.37553 (4n) %2b O (n n), and that Sylvester's Four Point Problem Constant is at least 0.37553. These improved bounds refine results recently obtained by Ábrego and Fernández-Merchant and by Lovász, Vesztergombi, Wagner, and Welzl.
abstract: We use circular sequences to give an improved lower bound on the minimum number of (≤ k)-sets in a set of points in general position. We then use this to show that if S is a set of n points in general position, then the number D(S) of convex quadrilaterals determined by the points in S is at least 0.37553(4n) %2b O(n3). This in turn implies that the rectilineal crossing number cr̄(Kn) of the complete graph Kn is at least 0.37553 (4n) %2b O (n n), and that Sylvester%27s Four Point Problem Constant is at least 0.37553. These improved bounds refine results recently obtained by Ábrego and Fernández-Merchant and by Lovász, Vesztergombi, Wagner, and Welzl.
date time value: article date 1642
estado: published
type: Thing
origen: scopus
type: Information Content Entity
volume: 35
doi: 10.1007/s00454-005-1227-6