Capacitated Vertex Cover admits no k^{o(k)} n^{O(1)} algorithm under ETH, n^{O(tw)} is optimal even for tree-depth, and vertex integrity admits a vi^{O(vi^2)} n^{O(1)} algorithm via N-fold IP.
Bodlaender and Carla Groenland and Hugo Jacob and Lars Jaffke and Paloma T
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Parameterized Capacitated Vertex Cover Revisited
Capacitated Vertex Cover admits no k^{o(k)} n^{O(1)} algorithm under ETH, n^{O(tw)} is optimal even for tree-depth, and vertex integrity admits a vi^{O(vi^2)} n^{O(1)} algorithm via N-fold IP.