W[1]-Hardness of the k-Center Problem Parameterized by the Skeleton Dimension

In the k-Center problem, we are given a graph \(G=(V,E)\) with positive edge weights and an integer k and the goal is to select k center vertices \(C \subseteq V\) such that the maximum distance from any vertex to the closest center vertex is minimized. On general graphs, the problem is NP-hard and cannot be approximated within a factor less than 2.