Obtaining a planar graph by vertex deletion

Abstract

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(n3) 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. © Springer-Verlag Berlin Heidelberg 2007.