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)


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.


Cactus Graphs Maximal Simple Path Pendent Cycles Witness Set Color Compatibility 
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.



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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