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(poly(k)logn) 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(poly(k)logn) bits