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?

authors

• Aichholzer O.
• Fernández-Merchant S.
• Leaños J.
• Salazar Anaya Gelasio
• Ábrego B.M.

publication date

• 2024-01-01

published in

• Ars Mathematica Contemporanea  Journal

keywords

• complete graphs; k-edges; Rectilinear crossing number

Digital Object Identifier (DOI)

• 10.26493/1855-3974.2763.1e6

PubMed ID

start page

end page

volume

• 24

issue

• 2