AI 中文总结
本文针对无限图提出Kriesell猜想的拓扑版本和$F$-极限版本，证明若有限图情形成立则对连通无射线有限边可分图成立，并给出生成树存在性结果。
AI 中文摘要
设$G$为一个图，$S\subseteq V(G)$为顶点子集。$G$的$S$-Steiner树$T$是$G$的一棵树，其顶点集$V(T)$包含$S$。Kriesell猜想：对于有限连通图$G$中每个$2k$-边连通的子集$S\subseteq V(G)$，存在$k$棵两两边不相交的$S$-Steiner树。该猜想对无限图为假。我们针对可数有限边可分图提出带拓扑$S$-Steiner树的Kriesell猜想版本，并针对无射线图提出带树$F$-极限的版本。我们证明：若Kriesell猜想对有限图成立，则它对每个连通、无射线且有限边可分的图成立。我们还证明：每个$2k$-边连通的无射线且有限边可分的图包含$k$棵两两边不相交的生成树。
英文摘要
Let $G$ be a graph and $S\subseteq V(G)$ be a subset of vertices. An $S$-Steiner tree $T$ of $G$ is a tree of $G$ which contains $S$ in its vertex set $V(T)$. Kriesell conjectured that for every $2k$-edge-connected subset $S\subseteq V(G)$ in a finite connected graph $G$, there exist $k$ pairwise edge-disjoint $S$-Steiner trees. This conjecture is false for infinite graphs. We present a version of Kriesell's conjecture with topological $S$-Steiner trees for countable finitely edge-separable graphs and a version with $F$-limits of trees for rayless graphs. We show that if Kriesell's conjecture holds for finite graphs, then it holds for every connected, rayless and finitely edge-separable graph. We also show that every $2k$-edge-connected rayless and finitely edge-separable graph contains $k$ pairwise edge-disjoint spanning trees.
