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The Parameterized Complexity of Graph Cyclability

  • Petr A. Golovach
  • Marcin Kamiński
  • Spyridon Maniatis
  • Dimitrios M. Thilikos
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8737)

Abstract

The cyclability of a graph is the maximum integer k for which every k vertices lie on a cycle. The algorithmic version of the problem, given a graph G and a non-negative integer k, decide whether the cyclability of G is at least k, is NP-hard. We prove that this problem, parameterized by k, is coW[1]-hard. We give an FPT algorithm for planar graphs that runs in time \(2^{2^{O(k^2\log k)}}\cdot n^2\). Our algorithm is based on a series of graph theoretical results on cyclic linkages in planar graphs.

Keywords

Planar Graph Parameterized Complexity Tree Decomposition Colored Vertex Graph Minor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Petr A. Golovach
    • 1
  • Marcin Kamiński
    • 2
  • Spyridon Maniatis
    • 3
  • Dimitrios M. Thilikos
    • 3
    • 4
  1. 1.Department of InformaticsUniversity of BergenBergenNorway
  2. 2.Institute of Computer ScienceUniversity of WarsawWarsawPoland
  3. 3.Department of MathematicsNational and Kapodistrian University of AthensAthensGreece
  4. 4.AlGCo project-team, CNRS, LIRMMMontpellierFrance

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