Faster deterministic parameterized algorithm for k-Path

In the k-Path problem, the input is a directed graph $G$ and an integer $k\geq 1$, and the goal is to decide whether there is a simple directed path in $G$ with exactly $k$ vertices. We give a deterministic algorithm for k-Path with time complexity $O^*(2.554k)$. This improves the previously best deterministic algorithm for this problem of Zehavi [ESA 2015] whose time complexity is $O^*(2.597k)$. The technique used by our algorithm can also be used to obtain faster deterministic algorithms for k-Tree, r-Dimensional k-Matching, Graph Motif, and Partial Cover.