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arXiv · 2301.06105

Long Directed Detours: Reduction to $2$-Disjoint Paths

Ashwin Jacob·Michał Włodarczyk·Meirav Zehavi
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Abstract

We study an "above guarantee" version of the {\sc Longest Path} problem in directed graphs: We are given a graph $G$, two vertices $s$ and $t$ of $G$, and a non-negative integer $k$, and the objective is to determine whether $G$ contains a path of length at least $dist_G(s,t) +k$ where $dist_G(s,t)$ is the length of a shortest path from $s$ to $t$ in $G$ (assuming that one exists). We show that the problem is fixed parameter tractable (FPT) parameterized by $k$ in the class of graphs where {\sc $2$-Disjoint Paths} problem is polynomial time solvable.

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Ashwin Jacob, Michał Włodarczyk, Meirav Zehavi. 2023-01-15. Long Directed Detours: Reduction to $2$-Disjoint Paths. https://arxiv.org/abs/2301.06105

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