Abstract
We provide first-time fixed-parameter tractability results for the NP-complete problems Maximum Full-Degree Spanning Tree and Minimum-Vertex Feedback Edge Set. These problems are dual to each other: In Maximum Full-Degree Spanning Tree, the task is to find a spanning tree for a given graph that maximizes the number of vertices that preserve their degree. For Minimum-Vertex Feedback Edge Set the task is to minimize the number of vertices that end up with a reduced degree. Parameterized by the solution size, we exhibit that Minimum-Vertex Feedback Edge Set is fixed-parameter tractable and has a problem kernel with the number of vertices linearly depending on the parameter k. Our main contribution for Maximum Full-Degree Spanning Tree, which is W[1]-hard, is a linear-size problem kernel when restricted to planar graphs. Moreover, we present subexponential-time algorithms in the case of planar graphs.
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Guo, J., Niedermeier, R., Wernicke, S. (2006). Fixed-Parameter Tractability Results for Full-Degree Spanning Tree and Its Dual. In: Bodlaender, H.L., Langston, M.A. (eds) Parameterized and Exact Computation. IWPEC 2006. Lecture Notes in Computer Science, vol 4169. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11847250_19
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DOI: https://doi.org/10.1007/11847250_19
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-39098-5
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