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.

翻译：在$K_r$覆盖问题中，给定图$G$和整数$k$，需要判断是否存在一个至多包含$k$个顶点的集合，使得移除这些顶点后能消除$G$中的所有$r$-团。本文提出了一种针对$K_r$覆盖问题的算法，该算法在满足与团和树宽相关的两个简单条件的图类上，可在子指数固定参数可处理时间内运行。作为应用，我们证明了该算法可在以下图类中以指定时间复杂度求解$K_r$覆盖问题：* 在伪圆盘图和地图图中，时间复杂度为$2^{O_r\left (k^{(r+1)/(r+2)}\log k \right)} \cdot n^{O_r(1)}$；* 在$K_{t,t}$-子图自由的字符串图中，时间复杂度为$2^{O_{t,r}(k^{2/3}\log k)} \cdot n^{O_r(1)}$；* 在$H$-次要自由图中，时间复杂度为$2^{O_{H,r}(k^{2/3}\log k)} \cdot n^{O_r(1)}$。