Obtaining a Planar Graph by Vertex Deletion
Abstract
Description
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, 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.
16 pages, 4 figures. A preliminary version of this paper appeared in the proceedings of WG 2007 (33rd International Workshop on Graph-Theoretic Concepts in Computer Science). The paper has been submitted to Algorithmica
16 pages, 4 figures. A preliminary version of this paper appeared in the proceedings of WG 2007 (33rd International Workshop on Graph-Theoretic Concepts in Computer Science). The paper has been submitted to Algorithmica