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

02/10/2023

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by   Takumi Tada, et al.

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For a set system (V,𝒞⊆ 2^V), we call a subset C∈𝒞 a component. A nonempty subset Y⊆ C is a minimal removable set (MRS) of C if C∖ Y∈𝒞 and no proper nonempty subset Z⊊ Y satisfies C∖ Z∈𝒞. In this paper, we consider the problem of enumerating all components in a set system such that, for every two components C,C'∈𝒞 with C'⊊ C, every MRS X of C satisfies either X⊆ C' or X∩ C'=∅. 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.