论文标题
正常跨越树木的新障碍物
A new obstruction for normal spanning trees
论文作者
论文摘要
在2001年的一篇论文（LMS期刊）中，Diestel和Leader提供了一个证据，证明连接图具有正常的生成树，并且仅当它不包含两个特定禁止类别的图表中的未成年人，所有的基数$ \ aleph_1 $。不幸的是，他们的证明包含差距，结果是不正确的。在本文中，我们构建了第三种类型的障碍物：$ \ aleph_1 $尺寸的图形没有正常的生成树，其中包含戴斯特尔（Diestel）和领导者（Leader）的两种类型。此外，我们表明，用正常跨越树的图表表征图形的任何禁止未成年人列表都必须包含任意大型基数的图形。
In a paper from 2001 (Journal of the LMS), Diestel and Leader offered a proof that a connected graph has a normal spanning tree if and only if it does not contain a minor from two specific forbidden classes of graphs, all of cardinality $\aleph_1$. Unfortunately, their proof contains a gap, and their result is incorrect. In this paper, we construct a third type of obstruction: an $\aleph_1$-sized graph without a normal spanning tree that contains neither of the two types described by Diestel and Leader as a minor. Further, we show that any list of forbidden minors characterising the graphs with normal spanning trees must contain graphs of arbitrarily large cardinality.
