Obtaining a Planar Graph by Vertex Deletion

  • Dániel Marx
  • Ildikó Schlotter
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4769)


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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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Dániel Marx
    • 1
  • Ildikó Schlotter
    • 2
  1. 1.Institut für Informatik, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099, BerlinGermany
  2. 2.Department of Computer Science and Information Theory, Budapest University of Technology and Economics, Budapest, H-1521Hungary

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