Résumé
In the K_r-Hitting 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-Hitting 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-Hitting in time - 2^{O_r(k^{(r+1)/(r+2)}log k)} ⋅ n^{O_r(1)} in pseudo-disk graphs and map-graphs; - 2^{O_{t,r}(k^{2/3}log k)} ⋅ n^{O_r(1)} in K_{t,t}-subgraph-free string graphs; and - 2^{O_{H,r}(k^{2/3}log k)} ⋅ n^{O_r(1)} in H-minor-free graphs.