There is a unique crossing-minimal rectilinear drawing of K_18

IF 0.6 3区数学 Q3 MATHEMATICS

Ars Mathematica Contemporanea Pub Date : 2023-06-28 DOI:10.26493/1855-3974.2763.1e6

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

引用次数: 0

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?

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K_18有一个独特的交叉最小直线图

我们证明，在有序型同构下，K18存在唯一的交叉最小直线图。很容易证实这张图不包含任何K17的交叉最小图。因此，这就否定地解决了Aichholzer和Krasser提出的以下问题:对于每一个整数n≥4，是否存在一个Kn的交叉极小图，其中包含一个Kn−1的交叉极小图?

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Ars Mathematica Contemporanea MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

1.70

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Ars mathematica contemporanea will publish high-quality articles in contemporary mathematics that arise from the discrete and concrete mathematics paradigm. It will favor themes that combine at least two different fields of mathematics. In particular, we welcome papers intersecting discrete mathematics with other branches of mathematics, such as algebra, geometry, topology, theoretical computer science, and combinatorics. The name of the journal was chosen carefully. Symmetry is certainly a theme that is quite welcome to the journal, as it is through symmetry that mathematics comes closest to art.