Résumé
The paper deals with the Feedback Vertex Set problem parameterized by the solution size. Given a graph G and a parameter k, one has to decide if there is a set S of at most k vertices such that G-S is acyclic. Assuming the Exponential Time Hypothesis, it is known that FVS cannot be solved in time $2^{o(k)}n^{\vartheta(1)}$ in general graphs. To overcome this, many recent results considered FVS restricted to particular intersection graph classes and provided such $2^{o(k)}n^{\vartheta(1)}$ algorithms.In this paper we provide generic conditions on a graph class for the existence of an algorithm solving FVS in subexponential FPT time, i.e. time $2^{k^{\varepsilon}}$ poly$(n)$, for some ${\varepsilon}<1$, where n denotes the number of vertices of the instance and k the parameter. On the one hand this result unifies algorithms that have been proposed over the years for several graph classes such as planar graphs, map graphs, unit-disk graphs, pseudo-disk graphs, and string graphs of bounded edge-degree. On the other hand it extends the tractability horizon of FVS to new classes that are not amenable to previously used techniques, in particular intersection graphs of "thin" objects like segment graphs or more generally s-string graphs.