Kick the cliques
<|reference_start|>Kick the cliques: In the $K_r$-Cover problem, given a graph $G$ and an integer $k$ one has to decide if there exists a set of at most $k$ vertices whose removal destroys all $r$-cliques of $G$. In this paper we give an algorithm for $K_r$-Cover that runs in subexponential FPT time on graph classes satisfying two simple conditions related to cliques and treewidth. As an application we show that our algorithm solves $K_r$-Cover in time   * $2^{O_r\left (k^{(r+1)/(r+2)}\log k \right)} \cdot n^{O_r(1)}$ in pseudo-disk graphs and map-graphs;   * $2^{O_{t,r}(k^{2/3}\log k)} \cdot n^{O_r(1)}$ in $K_{t,t}$-subgraph-free string graphs; and   * $2^{O_{H,r}(k^{2/3}\log k)} \cdot n^{O_r(1)}$ in $H$-minor-free graphs.<|reference_end|>
@article{berthe2024kick,
    title={Kick the cliques},
    author={Ga'etan Berthe, Marin Bougeret, Daniel Gonc{c}alves, Jean-Florent
  Raymond},
    journal={arXiv preprint arXiv:2407.01465},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.01465},
    primaryClass={cs.DS}
}