  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 $O^*(2.554^k)$. This improves the previously best
deterministic algorithm for this problem of Zehavi [ESA 2015] whose time
complexity is $O^*(2.597^k)$. 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.
