Let $G$ be an undirected graph, and $s,t$ distinguished vertices of $G$. A minimal $s,t$-separator is an inclusion-wise minimal vertex-set whose removal places $s$ and $t$ in distinct connected components. We present an algorithm for listing the minimal $s,t$-separators of a graph, whose cardinality is at most $k$, with FPT-delay, where the parameter depends only on $k$. This problem finds applications in various algorithms parameterized by treewidth, which include query evaluation in relational databases, probabilistic inference, and many more. We also present a simple algorithm that enumerates all of the (not necessarily minimal) $s,t$-separators of a graph in ranked order by size.

翻译：设 $G$ 为一个无向图，$s$ 和 $t$ 为 $G$ 中两个不同的顶点。极小 $s,t$-分隔符是一个按包含关系极小的顶点集，移除该集合后，$s$ 和 $t$ 处于不同的连通分量中。我们提出了一种算法，用于列出图中基数不超过 $k$ 的极小 $s,t$-分隔符，该算法具有 FPT-延迟（即固定参数可追踪延迟），其中参数仅依赖于 $k$。此问题在多种以树宽为参数的算法中有应用，包括关系数据库中的查询求值、概率推理等。此外，我们还提出了一种简单算法，可按大小排序枚举图中所有（不必是极小的）$s,t$-分隔符。