Before revision:  This problem has been considered in several articles in the last years. We focus on its kernelization , which had been almost unexplored so far. We prove that MMVC does not admit polynomial kernels parameterized by the size of a minimum vertex cover, even on bipartite graphs, unless NP \subseteq coNP / poly .
After revision:  Motivated by the kernelization of MMVC with parameter k, our main contribution is to introduce a simple general framework to obtain lower bounds on the degrees of a certain type of polynomial kernels for vertex optimization problems, which we call lop-kernels. Informally, this type of kernels is required to preserve large optimal solutions in the reduced instance, and captures the vast majority of existing kernels in the literature. As a consequence of this framework, we show that the trivial quadratic kernel for MMVC is essentially optimal, answering a minimum vertex cover, even on bipartite graphs, unless NP \subseteq coNP / poly .