论文标题
树状分类的规范树
Canonical trees of tree-decompositions
论文作者
论文摘要
我们证明，每个图都有一个规范的树分解树，可以有效地区分所有主要缠结（其中包括末端和各种大的有限密集结构）。 在这里，“树状分类的树”比“树状分类”略弱，但比“树状公制空间”更为良好。从某种意义上说，这种定理是最好的可能性，即我们举例说，“树木分解的树”不能加强到上述定理中的“树状分类”。 这意味着Dunwoody和Krön以及Carmesin，Diestel，Hundertmark和Stein的结果。除此之外，对于本地有限的图，我们的结果给出了\ Mathbb n $ canonical树的分类中的每个$ k \，可有效地区分所有$ k $ - 可区分的终点。
We prove that every graph has a canonical tree of tree-decompositions that distinguishes all principal tangles (these include the ends and various kinds of large finite dense structures) efficiently. Here `trees of tree-decompositions' are a slightly weaker notion than `tree-decompositions' but much more well-behaved than `tree-like metric spaces'. This theorem is best possible in the sense that we give an example that `trees of tree-decompositions' cannot be strengthened to `tree-decompositions' in the above theorem. This implies results of Dunwoody and Krön as well as of Carmesin, Diestel, Hundertmark and Stein. Beyond that for locally finite graphs our result gives for each $k\in\mathbb N$ canonical tree-decompositions that distinguish all $k$-distinguishable ends efficiently.
