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Discrete Mathematics
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publication venue for: Point sets that minimize (≤k)-edges, 3-decomposable drawings, and the rectilinear crossing number of K30
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Continuant
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RDF description of Point sets that minimize (≤k)-edges, 3-decomposable drawings, and the rectilinear crossing number of K30 - http://orbis.uaslp.mx/vivo/individual/scopus2835
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date: 2026-08-27T08:17:20
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Article
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Point sets that minimize (≤k)-edges, 3-decomposable drawings, and the rectilinear crossing number of K30
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type: Document
related by: authorship_16701
accesstype: All Open Access, Green
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type: Article
e iscopus: 2-s2.0-79959201514
estado: published
type: Generically Dependent Continuant
abstract: There are two properties shared by all known crossing-minimizing geometric drawings of Kn, for n a multiple of 3. First, the underlying n-point set of these drawings minimizes the number of (≤k)-edges, that means, has exactly 3(k 22)(≤k)-edges, for all 0≤k<n3. Second, all such drawings have the n points divided into three groups of equal size; this last property is captured under the concept of 3-decomposability. In this paper we show that these properties are closely related: every n-point set with exactly 3(k 22)(≤k)-edges for all 0≤k<n3, is 3-decomposable. The converse, however, is easy to see that it is false. As an application, we prove that the rectilinear crossing number of K30 is 9726. © 2011 Elsevier B.V. All rights reserved.
origen: scopus
most specific type: Article
doi: 10.1016/j.disc.2011.03.030
freetext keyword: 3-decomposability; k-edges; Rectilinear crossing number
volume: 311
most specific type: Document
abstract: There are two properties shared by all known crossing-minimizing geometric drawings of Kn, for n a multiple of 3. First, the underlying n-point set of these drawings minimizes the number of (≤k)-edges, that means, has exactly 3(k%2b22)(≤k)-edges, for all 0≤k<n3. Second, all such drawings have the n points divided into three groups of equal size; this last property is captured under the concept of 3-decomposability. In this paper we show that these properties are closely related: every n-point set with exactly 3(k%2b22)(≤k)-edges for all 0≤k<n3, is 3-decomposable. The converse, however, is easy to see that it is false. As an application, we prove that the rectilinear crossing number of K30 is 9726. © 2011 Elsevier B.V. All rights reserved.
crisid: 2836
type: Continuant
date time value: article date 2836
related by: authorship_16698
issue: 16
page start: 1646
related by: authorship_16700
related by: authorship_16699
page end: 1657
has publication venue: Discrete Mathematics

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