Romain Bourneuf

The coarse Erd\H{o}s-P\'{o}sa theorem

We prove the coarse Erd\H{o}s-P\'{o}sa conjecture of Georgakopoulos and Papasoglu. Informally, any graph either contains many fat cycles that are pairwise far apart, or there is a small number of bounded radius balls that together hit all of them. To be more precise, if $G$ is a graph with no $q$-fat model of $k \cdot...