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Partitioning Graphs into Induced Subgraphs

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Book cover Language and Automata Theory and Applications (LATA 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10168))

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Abstract

We study the Partition into \(H\) problem from the parametrized complexity point of view. In the Partition into \(H\) problem the task is to partition the vertices of a graph G into sets \(V_1,\dots ,V_r\) such that the graph H is isomorphic to the subgraph of G induced by each set \(V_i\) for \(i = 1,\dots ,r.\) The pattern graph H is fixed.

For the parametrization we consider three distinct structural parameters of the graph G – namely the tree-width, the neighborhood diversity, and the modular-width. For the parametrization by the neighborhood diversity we obtain an FPT algorithm for every graph H. For the parametrization by the tree-width we obtain an FPT algorithm for every connected graph H. Thus resolving an open question of Gajarský et al. from IPEC 2013 [9]. Finally, for the parametrization by the modular-width we derive an FPT algorithm for every prime graph H.

Research supported by the CE-ITI grant project P202/12/G061 of GA ČR, by GAUK project 1784214 and by the project SVV–2016–260332.

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Authors and Affiliations

  1. Department of Applied Mathematics, Charles University, Prague, Czech Republic

    Dušan Knop

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  1. Dušan Knop
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Correspondence to Dušan Knop .

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Editors and Affiliations

  1. Umeå University, Umeå, Sweden

    Frank Drewes

  2. Rovira i Virgili University, Tarragona, Spain

    Carlos Martín-Vide

  3. University of Giessen, Giessen, Germany

    Bianca Truthe

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Knop, D. (2017). Partitioning Graphs into Induced Subgraphs. In: Drewes, F., Martín-Vide, C., Truthe, B. (eds) Language and Automata Theory and Applications. LATA 2017. Lecture Notes in Computer Science(), vol 10168. Springer, Cham. https://doi.org/10.1007/978-3-319-53733-7_25

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  • DOI: https://doi.org/10.1007/978-3-319-53733-7_25

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  • Online ISBN: 978-3-319-53733-7

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