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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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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