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A Linear Kernel for Planar Feedback Vertex Set

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Parameterized and Exact Computation (IWPEC 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5018))

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Abstract

In this paper we show that Feedback Vertex Set on planar graphs has a kernel of size at most . We give a polynomial time algorithm, that given a planar graph G finds a equivalent planar graph G′ with at most vertices, where k * is the size of the minimum Feedback Vertex Set of G. The kernelization algorithm is based on a number of reduction rules. The correctness of most of these rules is shown using a new notion: bases of induced subgraphs. We also show how to use this new notion to automatically prove safeness of reduction rules and obtain tighter bounds for the size of the kernel.

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Authors and Affiliations

  1. Department of Information and Computing Sciences, Utrecht University, P.O. Box 80.089, 3508, TB Utrecht, The Netherlands

    Hans L. Bodlaender & Eelko Penninkx

Authors
  1. Hans L. Bodlaender
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  2. Eelko Penninkx
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Martin Grohe Rolf Niedermeier

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Bodlaender, H.L., Penninkx, E. (2008). A Linear Kernel for Planar Feedback Vertex Set. In: Grohe, M., Niedermeier, R. (eds) Parameterized and Exact Computation. IWPEC 2008. Lecture Notes in Computer Science, vol 5018. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79723-4_16

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  • DOI: https://doi.org/10.1007/978-3-540-79723-4_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-79722-7

  • Online ISBN: 978-3-540-79723-4

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