Abstract
In this paper we study the kernelization of the d-Path Vertex Cover (d-PVC) problem. Given a graph G, the problem requires finding whether there exists a set of at most k vertices whose removal from G results in a graph that does not contain a path (not necessarily induced) with d vertices. It is known that d-PVC is NP-complete for d≥2. Since the problem generalizes to d-Hitting Set, it is known to admit a kernel with O(dkd) edges. We improve on this by giving better kernels. Specifically, we give kernels with O(k2) vertices and edges for the cases when d=4 and d=5. Further, we give a kernel with O(k4d2d+9) vertices and edges for general d.
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