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In the k-Apex problem the task is to find at most k vertices whose deletion makes the given graph planar. The graphs for which there exists a solution form a minor closed class of graphs, hence by the deep results of Robertson and Seymour [34, 35] , there is a cubic algorithm for every fixed value of k. However, the proof is extremely complicated and the constants hidden by the big-O notation are huge. Here we give a much simpler algorithm for this problem with quadratic running time, bydoi:10.1007/978-3-540-74839-7_28 dblp:conf/wg/MarxS07 fatcat:yxc4ijtlvfc43ar4zbwxc35nva