Fat minors cannot be thinned (by quasi-isometries)

Abstract

We disprove the conjecture of Georgakopoulos and Papasoglu that a graph with no K -fat H minor is quasi-isometric to a graph with no H minor. On the other hand, we show that the following weakening holds: any graph with no K -fat H minor is quasi-isometric to a graph with no 3-fat H minor.