Résumé
For every$r\in \mathbb{N}$ , we denote by$\theta_{r}$the multigraph with two vertices and$r$parallel edges. Given a graph$G$ , we say that a subgraph$H$of$G$is a model of$\theta_{r}$in$G$if$H$contains$\theta_{r}$as a contraction. We prove that the following edge variant of the Erd os-Pósa property holds for every$r\geq 2$ : if$G$is a graph and$k$is a positive integer, then either$G$contains a packing of$k$mutually edge-disjoint models of$\theta_{r}$ , or it contains a set$S$of$f_r(k)$edges such that$G\setminus S$has no$\theta_{r}$ -model, for both$f_r(k) = O(k^2r^3 \mathrm{polylog}~kr)$and$f_r(k) = O(k^4r^2 \mathrm{polylog}~kr).$