On Andreae's ubiquity conjecture

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-09-01 DOI:10.1016/j.jctb.2023.04.002

Johannes Carmesin

引用次数: 1

Abstract

A graph H is ubiquitous if every graph G that for every natural number n contains n vertex-disjoint H-minors contains infinitely many vertex-disjoint H-minors. Andreae conjectured that every locally finite graph is ubiquitous. We give a disconnected counterexample to this conjecture. It remains open whether every connected locally finite graph is ubiquitous.

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关于Andreae的普遍性猜想

如果对于每个自然数n包含n个顶点不相交H-子的每个图G包含无限多个顶点不交H-子，则图H是普遍存在的。Andreae猜想每一个局部有限图都是普遍存在的。我们给这个猜想举了一个不连贯的反例。是否每一个连通的局部有限图都是普遍存在的，这仍然是开放的。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

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