We prove that for every integer t ⩾ 1 there exists a constant c_t such that for every K_t-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 c_t times the maximum number of vertex-disjoint balls in S. This was conjectured by Chepoi, Estellon, and Vaxès in 2007 in the special case of planar graphs and of balls having the same radius.

中文翻译：

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包装和覆盖图中未成年人的球

我们证明，对于每个整数吨⩾1存在一个常数C ^ _Ť使得对于每ķ_吨-minor -自由曲线图G ^，每一套小号在球ģ，一组顶点的最小尺寸ģ相交的所有的球小号是至多ç_吨次顶点不相交的球的最大数量小号。这是由Chepoi，Estellon和Vaxès在2007年对平面图和具有相同半径的球的特殊情况进行的推测。