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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 minimalremovable set (MRS) of $C$ if $C\setminus Y\in{\mathcal C}$ and no propernonempty subset $Z\subsetneq Y$ satisfies $C\setminus Z\in{\mathcal C}$. Inthis paper, we consider the problem of enumerating all components in a setsystem 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 all2-edge-connected induced subgraphs, and to enumerate all 2-vertex-connectedinduced subgraphs.

A Linear Delay Algorithm for Enumeration of 2-Edge/Vertex-connected Induced Subgraphs