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For every n ∈ N, there is a straight-line drawing Dn of a planar graph on n vertices such that in any crossing-free straight-line drawing of the graph, at most O(n.4982 ) vertices lie at the same position as in Dn . This improves on an earlier bound of O( √ n) by Goaoc et al.\u

Upper Bound Constructions for Untangling Planar Geometric Graphs