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.
Due to space constraints, the proofs of results marked with \(\star \) are omitted. These proof can be found in full version of the paper.
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Acknowledgements
We would like to thank Prof. Saket Saurabh for invaluable advice and several helpful suggestions.
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Krithika, R., Misra, P., Tale, P. (2018). An FPT Algorithm for Contraction to Cactus. In: Wang, L., Zhu, D. (eds) Computing and Combinatorics. COCOON 2018. Lecture Notes in Computer Science(), vol 10976. Springer, Cham. https://doi.org/10.1007/978-3-319-94776-1_29
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DOI: https://doi.org/10.1007/978-3-319-94776-1_29
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