Obtaining a planar graph by vertex deletion

Authors:
Dániel Marx;Ildikó Schlotter
Affiliations:
Institut für Informatik, Humboldt-Universität zu Berlin, Berlin, Germany;Department of Computer Science and Information Theory, Budapest University of Technology and Economics, Budapest, Hungary
Venue:
WG'07 Proceedings of the 33rd international conference on Graph-theoretic concepts in computer science
Year:
2007

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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.