  We present two new deterministic algorithms for the Feedback Vertex Set
problem parameterized by the solution size. We begin with a simple algorithm,
which runs in O*((2 + \phi)^k) time, where \phi < 1.619 is the golden ratio. It
already surpasses the previously fastest O*((1+2sqrt(2))^k)-time deterministic
algorithm due to Cao et al. [SWAT 2010]. In our developments we follow the
approach of Cao et al., however, thanks to a new reduction rule, we obtain not
only better dependency on the parameter in the running time, but also a
solution with simple analysis and only a single branching rule. Then, we
present a modification of the algorithm which, using a more involved set of
branching rules, achieves O*(3.592^k) running time.
