There is a unique crossing-minimal rectilinear drawing of K_18

Bernardo M. Ábrego; Silvia Fernández-Merchant; Oswin Aichholzer; Jesús Leaños; Gelasio Salazar

doi:10.26493/1855-3974.2763.1e6

There is a unique crossing-minimal rectilinear drawing of K_18

Bernardo M. Ábrego, Silvia Fernández-Merchant, Oswin Aichholzer, Jesús Leaños, Gelasio Salazar

Institute of Software Technology (7160)

Research output: Contribution to journal › Article › peer-review

Abstract

We show that, up to order type isomorphism, there is a unique crossing-minimal rectilinear drawing of K18. It is easily verified that this drawing does not contain any crossing-minimal drawing of K17. 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 crossing-minimal drawing of Kn that contains a crossing-minimal drawing of Kn − 1?

Original language	English
Number of pages	29
Journal	Ars Mathematica Contemporanea
Volume	24
Issue number	2
DOIs	https://doi.org/10.26493/1855-3974.2763.1e6
Publication status	Published - 2024

Fields of Expertise

Information, Communication & Computing

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10.26493/1855-3974.2763.1e6Licence: CC BY 4.0

Cite this

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AU - Leaños, Jesús

AU - Salazar, Gelasio

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DO - 10.26493/1855-3974.2763.1e6

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