论文标题
定向坦纳路径包装和定向路径连接
Directed Steiner path packing and directed path connectivity
论文作者
论文摘要
For a digraph $D=(V(D), A(D))$, and a set $S\subseteq V(D)$ with $r\in S$ and $|S|\geq 2$, a directed $(S, r)$-Steiner path or, simply, an $(S, r)$-path is a directed path $P$ started at $r$ with $S\subseteq V(P)$.如果没有共同的弧线，则两个$（s，r）$ - 据说它们是弧线 - 偶数。如果它们的一组普通顶点恰好是$ s $，则两个弧线 - 二十一个$（s，r）$ - 据说路径是内部不相交的。令$κ^p_ {s，r}（d）$（分别$λ^p_ {s，r}（d）$）是内部分离的最大数量（resp。Arc-disjoint）$（s，r）$ - $ d $中的路径。 The directed path $k$-connectivity of $D$ is defined as $$κ^p_k(D)= \min \{κ^p_{S,r}(D)\mid S\subseteq V(D), |S|=k, r\in S\}.$$ Similarly, the directed path $k$-arc-connectivity of $D$ is defined as $λ^p_k（d）= \ min \ {λ^p_ {s，r}（d）\ mid s \ mid s \ subseteq v（d），| s | = k，in s \}。图形可以看作是挖掘的经典连通性的概括。 在本文中，我们在Eulerian Digraphs和Symmetric Digraphs上获得了$κ^p_ {s，r}（d）$的复杂性结果，以及$λ^p_ {s，r}（d）$。我们还为参数提供界限$κ^p_k（d）$和$λ^p_k（d）$。
For a digraph $D=(V(D), A(D))$, and a set $S\subseteq V(D)$ with $r\in S$ and $|S|\geq 2$, a directed $(S, r)$-Steiner path or, simply, an $(S, r)$-path is a directed path $P$ started at $r$ with $S\subseteq V(P)$. Two $(S, r)$-paths are said to be arc-disjoint if they have no common arc. Two arc-disjoint $(S, r)$-paths are said to be internally disjoint if the set of common vertices of them is exactly $S$. Let $κ^p_{S,r}(D)$ (resp. $λ^p_{S,r}(D)$) be the maximum number of internally disjoint (resp. arc-disjoint) $(S, r)$-paths in $D$. The directed path $k$-connectivity of $D$ is defined as $$κ^p_k(D)= \min \{κ^p_{S,r}(D)\mid S\subseteq V(D), |S|=k, r\in S\}.$$ Similarly, the directed path $k$-arc-connectivity of $D$ is defined as $$λ^p_k(D)= \min \{λ^p_{S,r}(D)\mid S\subseteq V(D), |S|=k, r\in S\}.$$ The directed path $k$-connectivity and directed path $k$-arc-connectivity are also called directed path connectivity which extends the path connectivity on undirected graphs to directed graphs and could be seen as a generalization of classical connectivity of digraphs. In this paper, we obtain complexity results for $κ^p_{S,r}(D)$ on Eulerian digraphs and symmetric digraphs, and $λ^p_{S,r}(D)$ on general digraphs. We also give bounds for the parameters $κ^p_k(D)$ and $λ^p_k(D)$.
