  For a set system $(V,{\mathcal C}\subseteq 2^V)$, we call a subset
$C\in{\mathcal C}$ a component. A nonempty subset $Y\subseteq C$ is a minimal
removable set (MRS) of $C$ if $C\setminus Y\in{\mathcal C}$ and no proper
nonempty subset $Z\subsetneq Y$ satisfies $C\setminus Z\in{\mathcal C}$. In
this paper, we consider the problem of enumerating all components in a set
system such that, for every two components $C,C'\in{\mathcal C}$ with
$C'\subsetneq C$, every MRS $X$ of $C$ satisfies either $X\subseteq C'$ or
$X\cap C'=\emptyset$. We provide a partition-based algorithm for this problem,
which yields the first linear delay algorithms to enumerate all
2-edge-connected induced subgraphs, and to enumerate all 2-vertex-connected
induced subgraphs.
