Before revision:  Math. 2015] about the existence of subquadratic kernels for MMVC parameterized by k, we rule out their existence unless P=NP, if we restrict the kernelization algorithms to apply only a type of natural reduction rules that we call "large optimal preserving rules". In particular, these rules contain the typical reduction rules to obtain linear kernels for Vertex Cover .
After revision:  Math. 2015] , and that the known cubic kernel for Maximum Minimal Feedback Vertex Set is also essentially optimal .