Dips at small sizes for topological graph obstruction sets

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics Pub Date : 2024-09-12 DOI:10.1016/j.dam.2024.08.022

Hyoungjun Kim , Thomas W. Mattman

引用次数: 0

Abstract

The Graph Minor Theorem of Robertson and Seymour implies a finite set of obstructions for any minor closed graph property. We show that there are only three obstructions to knotless embedding of size 23, which is far fewer than the 92 of size 22 and the hundreds known to exist at larger sizes. We describe several other topological properties whose obstruction set demonstrates a similar dip at small size. For order ten graphs, we classify the 35 obstructions to knotless embedding and the 49 maximal knotless graphs.

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拓扑图阻碍集在小尺寸时的衰减

罗伯逊（Robertson）和西摩（Seymour）的 "图形次要定理"（Graph Minor Theorem of Robertson and Seymour）意味着任何次要封闭图形属性的障碍都是有限的。我们证明，大小为 23 的无结嵌入只有三个障碍，远远少于大小为 22 的 92 个障碍，也少于已知在更大大小时存在的数百个障碍。我们还描述了其他几种拓扑性质，它们的障碍集在小尺寸时也显示出类似的下降趋势。对于十阶图形，我们对 35 个无结嵌入障碍和 49 个最大无结图形进行了分类。

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

Discrete Applied Mathematics 数学-应用数学

CiteScore

2.30

自引率

9.10%

发文量

422

审稿时长

4.5 months

期刊介绍： The aim of Discrete Applied Mathematics is to bring together research papers in different areas of algorithmic and applicable discrete mathematics as well as applications of combinatorial mathematics to informatics and various areas of science and technology. Contributions presented to the journal can be research papers, short notes, surveys, and possibly research problems. The "Communications" section will be devoted to the fastest possible publication of recent research results that are checked and recommended for publication by a member of the Editorial Board. The journal will also publish a limited number of book announcements as well as proceedings of conferences. These proceedings will be fully refereed and adhere to the normal standards of the journal. Potential authors are advised to view the journal and the open calls-for-papers of special issues before submitting their manuscripts. Only high-quality, original work that is within the scope of the journal or the targeted special issue will be considered.