Faster deterministic Feedback Vertex Set

• Faster deterministic FPT algorithm for Feedback Vertex Set.
• Reinterpretation and simplification of the previously best algorithm for FVS.
• Simpler proof that FVS becomes polynomial-time solvable in subcubic graphs.

We present a new deterministic algorithm for the Feedback Vertex Set problem parameterized by the solution size. Our algorithm runs in O⁎((2+ϕ)k)O⁎((2+ϕ)k) time, where ϕ<1.619ϕ<1.619 is the golden ratio, surpassing the previously fastest O⁎((1+22)k)-time deterministic algorithm due to Cao et al. (2010) [6]. In our development 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.