Let $G=(V,E))$ be a directed graph. A $2$-edge-twinless block in $G$ is a maximal vertex set $C^{t}\subseteq V$ of with $|C^{t}|>1$ such that for any distinct vertices $v,w \in C^{t}$, and for every edge $e\in E$, the vertices $v,w$ are in the same twinless strongly connected component of $G\setminus\left \lbrace e \right\rbrace $. An edge $e$ in a twinless strongly connected graph is a twinless bridge if the subgraph obtained from $G$ by removing $e$ is not twinless strongly connected. In this paper we show that the $2$-edge-twinless blocks of $G$ can be computed in $O((b_{t}n+m)n)$ time, where $b_{t}$ is the number of twinless bridges of $G$.
翻译:Let $G = (V,E) 是一个定向图表。$G$中的2美元双向无双方块是一个最高顶点,用$C$,t ⁇ subsetequ V$,用$C$,t ⁇ 1$,这样,对于任何不同的顶点,用$V,w c ⁇ t}美元,对于每一边的E$,顶点值为$Setminus\left e\lbrace e\right\rbrace $。双重连接图中的边值美元,如果从$G$中去除的分数不是无双向的,则双向双向桥。在本文中我们表明,$2美元的顶点无双向区块可以用$((b ⁇ n+m)n时间计算,其中$b ⁇ t}是无双向G$的双向桥数。