论文标题
图III中的普遍性：局部有限图的无处不在，带有广泛的树分类
Ubiquity in graphs III: Ubiquity of locally finite graphs with extensive tree-decompositions
论文作者
论文摘要
图形$ g $据说无处不在，如果每个图形$γ$都包含任意的许多不相交$ g $ -Minors会自动包含无限的许多脱节$ G $ -Minors。众所周知的无处不在安德里亚（Andreae）表明，每个本地有限的图都无处不在。 在本文中，我们表明，本地有限的图表承认某种类型的树分解，我们称之为广泛的树分解，无处不在。特别是，这包括有限树宽度的所有本地有限图，以及所有局部有限的图表，所有末端都有有限的末端。是否每个本地有限的图都允许广泛的树状分解，这仍然是一个悬而未决的问题。
A graph $G$ is said to be ubiquitous, if every graph $Γ$ that contains arbitrarily many disjoint $G$-minors automatically contains infinitely many disjoint $G$-minors. The well-known Ubiquity conjecture of Andreae says that every locally finite graph is ubiquitous. In this paper we show that locally finite graphs admitting a certain type of tree-decomposition, which we call an extensive tree-decomposition, are ubiquitous. In particular this includes all locally finite graphs of finite tree-width, and also all locally finite graphs with finitely many ends, all of which have finite degree. It remains an open question whether every locally finite graph admits an extensive tree-decomposition.
