FPT-space Graph Kernelizations

Let $n$ be the size of a parametrized problem and $k$ the parameter. We present a full kernel for Path Contraction and Cluster Editing/Deletion as well as a kernel for Feedback Vertex Set whose sizes are all polynomial in $k$, that are computable in polynomial time, and use $O(\rm{poly}(k) \log n)$ bits. By first executing the new kernelizations and subsequently the best known polynomial-time kernelizations for the problem under consideration, we obtain the best known kernels in polynomial time with $O(\rm{poly}(k) \log n)$ bits.