On the complexity of vertex-disjoint length-restricted path problems

@article{Bley2003OnTC,
  title={On the complexity of vertex-disjoint length-restricted path problems},
  author={Andreas Bley},
  journal={computational complexity},
  year={2003},
  volume={12},
  pages={131-149}
}
Abstract Let $G=(V,E)$ be a simple graph and $s$ and $t$ be two distinct vertices of $G$. A path in $G$ is called \lb for some $\length\in\N$ if it does not contain more than $\length$ edges. We prove that computing the maximum number of \vd \lb $s,t$-paths is \apx--complete for any $\length\geq 5$. This implies that the problem of finding $k$ \vd \lb $s,t$-paths with minimal total weight for a given number $k\in\N$, $1\leq k \leq |V|-1$, and nonnegative weights on the edges of $G$ is \npo… CONTINUE READING