Obtaining a Planar Graph by Vertex Deletion
In the Planar + k vertex 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 [19,18], there is an O(n 3) time 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, by iteratively reducing the input graph and then applying techniques for graphs of bounded treewidth.
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