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    Kernelization using structural parameters on sparse graph classes

    Gajarský, J. and Hlinený, P. and Obdrzálek, J. and Ordyniak, S. and Reidl, Felix and Rossmanith, P. and Sánchez Villaamil, F. and Sikdar, S. (2016) Kernelization using structural parameters on sparse graph classes. Journal of Computer and System Sciences 84 , pp. 219-242. ISSN 0022-0000.

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    Abstract

    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.

    Metadata

    Item Type: Article
    School: Birkbeck Schools and Departments > School of Business, Economics & Informatics > Computer Science and Information Systems
    Depositing User: Felix Reidl
    Date Deposited: 26 Oct 2018 07:09
    Last Modified: 26 Oct 2018 07:09
    URI: http://eprints.bbk.ac.uk/id/eprint/24755

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