Various algorithms have been proposed to enumerate all connected induced subgraphs of a graph $G=(V,E)$. As a variation we enumerate all "conn-partitions", i.e. partitions $\Pi$ of $V$ with the property that each part of $\Pi$ induces a connected subgraph. In another vein, we enumerate all $X\subseteq V$ which induce a subgraph that is (respectively) chordal, bipartite, or a forest. Mentioned four algorithms, and two more, run in ouput-polynomial time (and deliver their fare in compressed fashion). Along the way we give fresh and short proofs of well-known facts about bipartite graphs and chordless cycles respectively.

翻译：已有多种算法被提出用于枚举图$G=(V,E)$的所有连通诱导子图。作为一种变体，我们枚举所有"连通划分"，即满足每个划分块均诱导出连通子图的划分$\Pi$。另一方面，我们枚举所有诱导子图分别为弦图、二分图或森林的顶点子集$X\subseteq V$。所提及的四种算法及另外两种算法均以输出多项式时间运行（并以压缩形式输出结果）。在此过程中，我们分别针对二分图和无弦环给出了简洁新颖的经典结论证明。