Let $G=(V,E)$ be a strongly connected graph with $|V|\geq 3$. For $T\subseteq V$, the strongly connected graph $G$ is $2$-T-connected if $G$ is $2$-edge-connected and for each vertex $w$ in $T$, $w$ is not a strong articulation point. This concept generalizes the concept of $2$-vertex connectivity when $T$ contains all the vertices in $G$. This concept also generalizes the concept of $2$-edge connectivity when $|T|=0$. The concept of $2$-T-connectivity was introduced by Durand de Gevigney and Szigeti in $2018$. In this paper, we prove that there is a polynomial-time 4-approximation algorithm for the following problem: given a $2$-T-connected graph $G=(V,E)$, identify a subset $E^ {2T} \subseteq E$ of minimum cardinality such that $(V,E^{2T})$ is $2$-T-connected.

翻译：设$G=(V,E)$是一个强连通图，满足$|V|\geq 3$。对于$T\subseteq V$，强连通图$G$是2-T连通的，如果$G$是2-边连通的，并且对于$T$中的每个顶点$w$，$w$都不是强关节点。当$T$包含$G$中的所有顶点时，此概念推广了2-顶点连通性的概念。当$|T|=0$时，此概念也推广了2-边连通性的概念。2-T连通性的概念由Durand de Gevigney和Szigeti于2018年引入。在本文中，我们证明对于以下问题存在多项式时间的4-近似算法：给定一个2-T连通图$G=(V,E)$，找出一个最小基数的子集$E^{2T} \subseteq E$，使得$(V,E^{2T})$是2-T连通的。