We prove that for every integer t≥1 there exists a constant ct such
that for every Kt-minor-free graph G, and every set S of balls in G,
the minimum size of a set of vertices of G intersecting all the balls of S
is at most ct times the maximum number of vertex-disjoint balls in S. This
was conjectured by Chepoi, Estellon, and Vax\`es in 2007 in the special case of
planar graphs and of balls having the same radius.Comment: v3: final versio