论文标题
$ 2 $ - 块在强烈双连接的定向图中
$2$-blocks in strongly biconnected directed graphs
论文作者
论文摘要
如果$ g $连接$ g $，并且$ g $的基础图是双连接的，则指示图$ g =（v，e）$被称为强烈双连接。强烈连接的图形$ g =（v，e）$的强烈双连接组件是最大顶点子集$ l \ subseteq v $，因此$ l $上的诱导子图是强烈的。令$ g =（v，e）$是一个强烈双连接的有向图。 $ g $中的$ 2 $ - 边缘双连接块是最大顶点子集$ u \ subseteq v $，以便在任何两个差异的co $ v，w \ in u $中，对于e $ in e $的每个边缘$ b \ in e $，fertices $ v，w $ w $属于同样的$ g \ g lbrace $ g \ lbrace ush y rbrace ush y y lbrace brace ry \ ry \ ry \ ry \ y ry \ y \ ry \ y ry \ y ry \ ry \ y \ y \ y \ y ry。 $ g $中的$ 2 $ - strong-biconnected块是一个最大顶点子集$ u \ subseteq v $的大小至少$ 2 $，以便每双不同的顶点$ v，w \ in u $ in u $ in u $ in u $ in u $，并且每个顶点$ z \ in v \ setminus \ setminus \ lestminus \ lbrace v $ weft \ lbrace $， $ g \ setminus \ left \ lbrace v，w \ right \ rbrace $的强烈双连接组件。在本文中，我们研究了$ 2 $ - 边缘双连接的块和$ 2 $ strong双连接块。
A directed graph $G=(V,E)$ is called strongly biconnected if $G$ is strongly connected and the underlying graph of $G$ is biconnected. A strongly biconnected component of a strongly connected graph $G=(V,E)$ is a maximal vertex subset $L\subseteq V$ such that the induced subgraph on $L$ is strongly biconnected. Let $G=(V,E)$ be a strongly biconnected directed graph. A $2$-edge-biconnected block in $G$ is a maximal vertex subset $U\subseteq V$ such that for any two distict vertices $v,w \in U$ and for each edge $b\in E$, the vertices $v,w$ are in the same strongly biconnected components of $G\setminus\left\lbrace b\right\rbrace $. A $2$-strong-biconnected block in $G$ is a maximal vertex subset $U\subseteq V$ of size at least $2$ such that for every pair of distinct vertices $v,w\in U$ and for every vertex $z\in V\setminus\left\lbrace v,w \right\rbrace $, the vertices $v$ and $w$ are in the same strongly biconnected component of $G\setminus \left\lbrace v,w \right\rbrace $. In this paper we study $2$-edge-biconnected blocks and $2$-strong biconnected blocks.
