Point sets that minimize <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si118.gif" display="inline" overflow="scroll"><mml:mrow><mml:mo>(</mml:mo><mml:mo>≤</mml:mo><mml:mi>k</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>-edges, 3-decomposable drawings, and the rectilinear crossing number of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1095.gif" display="inline" overflow="scroll"><mml:msub><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mn>30</mml:mn></mml:mro

Cetina, M.; Hernández-Vélez, César; Leaños, Jesús; Villalobos, C.I

doi:10.1016/j.disc.2011.03.030

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Cited by 10 publications

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“…In this work we finally have given the full proof of Theorem 1.2, which was announced at the EuroComb'11 conference [1]. As we mentioned in the Introduction, the exact rectilinear crossing number of K n is known only for n ≤ 27 and n = 30 [3,7,8,9,10]. In [2] and [6] we can find nonisomorphic crossing-minimal rectilinear drawings of K n for both n = 24 and n = 30.…”

Section: Discussionmentioning

confidence: 99%

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There is a unique crossing-minimal rectilinear drawing of K_18

Ábrego,

Fernández-Merchant,

Aichholzer

et al. 2024

Ars Math. Contemp.

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We show that, up to order type isomorphism, there is a unique crossing-minimal rectilinear drawing of K 18 . It is easily verified that this drawing does not contain any crossingminimal drawing of K 17 . Therefore this settles, in the negative, the following question from Aichholzer and Krasser: is it true that, for every integer n ≥ 4, there exists a crossingminimal drawing of K n that contains a crossing-minimal drawing of K n−1 ?

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