论文标题
正常跨越树的统一存在定理
A unified existence theorem for normal spanning trees
论文作者
论文摘要
我们证明，当且仅当其顶点集是由有限的一组顶点与任何细分的无限集团分离的，每个集合与任何细分的无限集团分开时，图形$ g $具有正常的生成树。这证明了Brochet和Diestel从1994年开始的猜想，从而使两个经典的正常生成树标准的共同加强。 此外，我们的方法给出了Halin定理的一种新的算法证明，即每个连接的图形不包含一个可计数集团的细分都具有正常的生成树。
We show that a graph $G$ has a normal spanning tree if and only if its vertex set is the union of countably many sets each separated from any subdivided infinite clique in $G$ by a finite set of vertices. This proves a conjecture by Brochet and Diestel from 1994, giving a common strengthening of two classical normal spanning tree criterions due to Jung and Halin. Moreover, our method gives a new, algorithmic proof of Halin's theorem that every connected graph not containing a subdivision of a countable clique has a normal spanning tree.
