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Kernelization using structural parameters on sparse graph classes

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GAJARSKÝ Jakub HLINĚNÝ Petr OBDRŽÁLEK Jan ORDYNIAK Sebastian REIDL Felix ROSSMANITH Peter VILLAAMIL Fernando SIKDAR Somnath

Druh Článek v odborném periodiku
Časopis / Zdroj Journal of Computer and System Sciences
Fakulta / Pracoviště MU

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Citace
Doi http://dx.doi.org/10.1016/j.jcss.2016.09.002
Obor Informatika
Klíčová slova Parameterized complexity; Kernelization; Nowhere dense graphs; Finite integer index; Treedepth
Popis We prove that graph problems with finite integer index have linear kernels on graphs of bounded expansion when parameterized by the size of a modulator to constant-treedepth graphs. For nowhere dense graph classes, our result yields almost-linear kernels. We also argue that such a linear kernelization result with a weaker parameter would fail to include some of the problems covered by our framework. We only require the problems to have FII on graphs of constant treedepth. This allows to prove linear kernels also for problems such as Longest-Path/Cycle, Exact-s, t-Path, Treewidth, and Pathwidth, which do not have FII on general graphs. (C) 2016 Elsevier Inc. All rights reserved.
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