, Volume 62, Issue 3–4, pp 807–822 | Cite as

Obtaining a Planar Graph by Vertex Deletion

  • Dániel Marx
  • Ildikó Schlotter


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 (J. Comb. Theory, Ser. B 63(1):65–110, 1995; J. Comb. Theory, Ser. B 92(2):325–357, 2004), there is a cubic 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.


Planar graph Apex graph FPT algorithm Vertex deletion 


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© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of Computer Science and Information TheoryBudapest University of Technology and EconomicsBudapestHungary

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