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On the Small Cycle Transversal of Planar Graphs

  • Ge Xia
  • Yong Zhang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6410)

Abstract

We consider the problem of finding a k-edge transversal set that intersects all (simple) cycles of length at most s in a planar graph, where s ≥ 3 is a constant. This problem, referred to as Small Cycle Transversal, is known to be NP-complete. We present a polynomial-time algorithm that computes a kernel of size 36 s 3 k for Small Cycle Transversal. In order to achieve this kernel, we extend the region decomposition technique of Alber et al. [J. ACM, 2004 ] by considering a unique region decomposition that is defined by shortest paths. Our kernel size is an exponential improvement in terms of s over the kernel size obtained under the meta-kernelization framework by Bodlaender et al. [FOCS, 2009 ].

Keywords

Parameterized Complexity Kernelization Planar Graphs Cycle Transversal 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Ge Xia
    • 1
  • Yong Zhang
    • 2
  1. 1.Department of Computer ScienceLafayette CollegeEastonUSA
  2. 2.Department of Computer ScienceKutztown UniversityKutztownUSA

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