Abstract
Every connected graph on n vertices has a cut of size at least \(n-1\). We call this bound the ‘spanning tree bound’. In the Max-Cut Above Spanning Tree (Max-Cut-AST) problem, we are given a connected n-vertex graph G and a non-negative integer k, and the task is to decide whether G has a cut of size at least \(n-1+k\). We show that Max-Cut-AST admits an algorithm that runs in time \(\mathcal {O}(8^kn^{\mathcal {O}(1)})\), and hence it is fixed parameter tractable with respect to k. Furthermore, we show that Max-Cut-AST has a polynomial kernel of size \(\mathcal {O}(k^5)\).
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Madathil, J., Saurabh, S., Zehavi, M. (2018). Max-Cut Above Spanning Tree is Fixed-Parameter Tractable. In: Fomin, F., Podolskii, V. (eds) Computer Science – Theory and Applications. CSR 2018. Lecture Notes in Computer Science(), vol 10846. Springer, Cham. https://doi.org/10.1007/978-3-319-90530-3_21
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DOI: https://doi.org/10.1007/978-3-319-90530-3_21
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