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The 2-Vertex-Connected Spanning Subgraph problem (2VCSS) is among the mostbasic NP-hard (Survivable) Network Design problems: we are given an(unweighted) undirected graph $G$. Our goal is to find a subgraph $S$ of $G$with the minimum number of edges which is $2$-vertex-connected, namely $S$remains connected after the deletion of an arbitrary node. 2VCSS iswell-studied in terms of approximation algorithms, and the current best(polynomial-time) approximation factor is $10/7$ by Heeger and Vygen [SIDMA'17](improving on earlier results by Khuller and Vishkin [STOC'92] and Garg,Vempala and Singla [SODA'93]).

A $4/3$ Approximation for $2$-Vertex-Connectivity