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

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