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arXiv · 2211.07001

Kernelization for Partial Vertex Cover via (Additive) Expansion Lemma

Tomohiro Koana·André Nichterlein·Niklas Wünsche
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Abstract

Given a graph and two integers $k$ and $\ell$, Partial Vertex Cover asks for a 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 of the expansion lemma and show it can be used to prove a kernel with $(\ell + 1)(k + \ell)$ vertices for $\ell \ge 1$.

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Tomohiro Koana, André Nichterlein, Niklas Wünsche. 2022-11-13. Kernelization for Partial Vertex Cover via (Additive) Expansion Lemma. https://arxiv.org/abs/2211.07001

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