Parameterized Algorithms for Even Cycle Transversal

  • Pranabendu Misra
  • Venkatesh Raman
  • M. S. Ramanujan
  • Saket Saurabh
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7551)

Abstract

We consider a decision version of the problem of finding the minimum number of vertices whose deletion results in a graph without even cycles. While this problem is a natural analogue of the Odd Cycle Transversal problem (which asks for a subset of vertices to delete to make the resulting graph bipartite), surprisingly this problem is not well studied. We first observe that this problem is NP-complete and give a constant factor approximation algorithm. Then we address the problem in parameterized complexity framework with the solution size k as a parameter. We give an algorithm running in time O*(2O(k)) for the problem and give an O(k2) vertex kernel. (We write O*(f(k)) for a time complexity of the form O(f(k)nO(1)), where f (k) grows exponentially with k.)

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Pranabendu Misra
    • 2
  • Venkatesh Raman
    • 1
  • M. S. Ramanujan
    • 1
  • Saket Saurabh
    • 1
  1. 1.The Institute of Mathematical SciencesChennaiIndia
  2. 2.Chennai Mathematical InstituteIndia

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