标题： 渐近结构。 III。 排除一个肥树 显示英文标题

标题： Asymptotic structure. III. Excluding a fat tree

摘要： 罗伯逊和塞缪尔证明了对于每个有限树$H$，存在$k$，使得每个没有$H$矿物的有限图$G$的路径宽度最多为$k$；反之，对于每个整数$k$，存在一个有限树$H$，使得每个具有$H$矿物的有限图$G$的路径宽度超过$k$。 如果我们两次将“路径宽度”替换为“线宽度”，那么对于无限图$G$也是如此。我们证明了一个“粗略图论”的类似结论，如下所示。 对于每个有限树$H$和每个$c$，存在$k,L,C$使得不包含$H$作为$c$-fat 小图的每个图都允许到一个线宽至多为$k$的图的$(L,C)$-近似同构；反之，对于所有$k,L,C$，存在$c$和一个有限树$H$，使得包含$H$作为$c$-fat 小图的每个图都不允许到一个线宽至多为$k$的图的$(L,C)$-近似同构。 显示英文摘要

摘要： Robertson and Seymour proved that for every finite tree $H$, there exists $k$ such that every finite graph $G$ with no $H$ minor has path-width at most $k$; and conversely, for every integer $k$, there is a finite tree $H$ such that every finite graph $G$ with an $H$ minor has path-width more than $k$. If we (twice) replace ``path-width'' by ``line-width'', the same is true for infinite graphs $G$. We prove a ``coarse graph theory'' analogue, as follows. For every finite tree $H$ and every $c$, there exist $k,L,C$ such that every graph that does not contain $H$ as a $c$-fat minor admits an $(L,C)$-quasi-isonetry to a graph with line-width at most $k$; and conversely, for all $k,L,C$ there exist $c$ and a finite tree $H$ such that every graph that contains $H$ as a $c$-fat minor admits no $(L,C)$-quasi-isometry to a graph with line-width at most $k$.