Abstract
We try to describe in this paper how methods from extremal combinatorics play an important role in the development of parameterized algorithms, also sketching further venues how this influence could be even increased in order to obtain quick \(\mathcal {FPT}\) classification results. Conversely, we show how certain notions that have become of importance within parameterized algorithmics can be useful to keep in mind for combinatorialists. We hope that this account initiates fruitful future discussions between the different scientific sub-communities that usually comprise IWOCA and that make this event quite special.
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Notes
- 1.
For related results, we refer to P. Valtr’s paper in this proceedings.
- 2.
Further examples can be found in the paper of V. Lozin in this proceedings.
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Acknowledgements
This paper has profited a lot from discussions we had with many colleagues, in particular, with Faisal Abu-Khzam, Ljiljana Brankovic and Mike Fellows. Thanks to Frances Rosamond and Ulrike Stege for proofreading.
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Fernau, H. (2018). Extremal Kernelization: A Commemorative Paper. In: Brankovic, L., Ryan, J., Smyth, W. (eds) Combinatorial Algorithms. IWOCA 2017. Lecture Notes in Computer Science(), vol 10765. Springer, Cham. https://doi.org/10.1007/978-3-319-78825-8_3
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