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Given a graph and two integers $k$ and $\ell$, Partial Vertex Cover asks fora set of at most $k$ vertices whose deletion results in a graph with at most$\ell$ edges. Based on the expansion lemma, we provide a problem kernel with$(\ell + 2)(k + \ell)$ vertices. We then introduce a new, additive version ofthe expansion lemma and show it can be used to prove a kernel with $(\ell +1)(k + \ell)$ vertices for $\ell \ge 1$.

Kernelization for Partial Vertex Cover via (Additive) Expansion Lemma