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A geometric graph is a graph drawn in the plane such that its edges are closed line segments and no three vertices are collinear. We settle an old question of Avital, Hanani, Erd~s, Kupitz, and Perles by showing that every geometric graph with n vertices and m > k4n edges contains k + 1 pairwise disjoint edges. We also prove that, given a set of points V and a set of axis-parallel rectangles in the plane, then either there are k + 1 rectangles such that no point of V belongs to more than one ofdoi:10.1007/bf02574361 fatcat:syigyh5vujevfdv4proqmrp67i