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Partitioning Graphs into Induced Subgraphs

  • Dušan KnopEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10168)

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.

Keywords

Generalized matching Parametrized complexity 

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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Applied MathematicsCharles UniversityPragueCzech Republic

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