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.

中文翻译：

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关于 Andreae 的无处不在猜想

如果每个自然数n包含n 个顶点不相交的H -minors的每个图G包含无限多个顶点不相交的H -minors，则图H是无处不在的。Andreae 推测每个局部有限图都是普遍存在的。我们给这个猜想一个不相关的反例。每个连接的局部有限图是否普遍存在仍然是开放的。