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Obtaining a Planar Graph by Vertex Deletion

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Abstract

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.

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Authors and Affiliations

  1. Department of Computer Science and Information Theory, Budapest University of Technology and Economics, Budapest, 1521, Hungary

    Dániel Marx & Ildikó Schlotter

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  1. Dániel Marx
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  2. Ildikó Schlotter
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Correspondence to Ildikó Schlotter.

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Supported by the Hungarian National Research Fund OTKA 67651.

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Marx, D., Schlotter, I. Obtaining a Planar Graph by Vertex Deletion. Algorithmica 62, 807–822 (2012). https://doi.org/10.1007/s00453-010-9484-z

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  • DOI: https://doi.org/10.1007/s00453-010-9484-z

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