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Lecture Notes in Computer Science
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publication venue for: Improved bounds for the number of (≤ k)-Sets, convex quadrilaterals, and the rectilinear crossing number of Kn
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Generically Dependent Continuant
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RDF description of Improved bounds for the number of (≤ k)-Sets, convex quadrilaterals, and the rectilinear crossing number of Kn - http://orbis.uaslp.mx/vivo/individual/scopus8329
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date: 2026-08-27T08:17:22
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Article
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Information Content Entity
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Improved bounds for the number of (≤ k)-Sets, convex quadrilaterals, and the rectilinear crossing number of Kn
type: Document
related by: authorship_54100
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 □ (S) of convex quadrilaterals determined by the points in S is at least 0.37553(4n) O(n3). This in turn implies that the rectilinear crossing number ̄cr(Kn) of the complete graph Kn is at least 0.37553(4n) O(n3). These improved bounds refine results recently obtained by Abrego and Fernández-Merchant, and by Lovász, Vesztergombi, Wagner and Welzl. © Springer-Verlag Berlin Heidelberg 2004.
origen: scopus
date time value: conference paper date 8330
type: Article
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 □ (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 rectilinear crossing number ̄cr(Kn) of the complete graph Kn is at least 0.37553(4n) %2b O(n3). These improved bounds refine results recently obtained by Abrego and Fernández-Merchant, and by Lovász, Vesztergombi, Wagner and Welzl. © Springer-Verlag Berlin Heidelberg 2004.
volume: 3383
page start: 25
estado: published
freetext keyword: Boundary conditions; Computer science; Mathematical models; Artificial intelligence; Computer science; Computers; Circular sequences; Convex quadrilaterals; Rectilinear crossing numbers; Graph theory; Drawing (graphics); Circular sequences; Complete graphs; Convex quadrilaterals; Lower bounds; Points in general position; Rectilinear crossing numbers
type: Information Content Entity
EI dscopus: 2-s2.0-24144482643
type: Conference Paper
has publication venue: Lecture Notes in Computer Science
crisid: 8330
type: Generically Dependent Continuant
type: Entity
related by: authorship_54099
page end: 35
type: Continuant
most specific type: Conference Paper
type: Thing

Conference Paper
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