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An FPT Algorithm for Contraction to Cactus

  • R. Krithika
  • Pranabendu Misra
  • Prafullkumar TaleEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10976)

Abstract

For a collection \(\mathcal {F}\) of graphs, given a graph G and an integer k, the \(\mathcal {F}\)-Contraction problem asks whether we can contract k edges in G to obtain a graph in \(\mathcal {F}\). \(\mathcal {F}\)-Contraction is well studied and known to be C-complete for several classes \(\mathcal {F}\). Heggerners et al. [Algorithmica (2014)] were the first to explicitly study contraction problems in the realm of parameterized complexity. They presented FPT algorithms for Tree-Contraction and Path-Contraction. In this paper, we study contraction to a class larger than trees, namely, cactus graphs. We present an FPT algorithm for Cactus-Contraction that runs in \(c^kn^{\mathcal {O}(1)}\) time for some constant c.

Notes

Acknowledgements

We would like to thank Prof. Saket Saurabh for invaluable advice and several helpful suggestions.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • R. Krithika
    • 1
  • Pranabendu Misra
    • 2
  • Prafullkumar Tale
    • 1
    Email author
  1. 1.The Institute of Mathematical SciencesHBNIChennaiIndia
  2. 2.Department of InformaticsUniversity of BergenBergenNorway

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