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(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.

• Type: Conference
• Year: 2007
• Where: WG
• Authors: Dániel Marx, Ildikó Schlotter
• Keywords: Computer Science, Graph Planar, Minor Closed Class, Planar +k Vertex, WG 2007