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We prove that the complement of any non-separating planar graph of order$2n-3$ contains a $K_n$ minor, and argue that the order $2n-3$ is lowestpossible with this property. To illustrate the necessity of the non-separatinghypothesis, we give an example of a planar graph of order 11 whose complementdoes not contain a $K_7$ minor. We argue that the complements of planar graphsof order 11 are intrinsically knotted. We compute the Hadwiger numbers ofcomplements of wheel graphs.

Complete Minors in Complements of Non-Separating Planar Graphs