Partitioning Graphs into Induced Subgraphs

Abstract

We study the Partition into H problem from the parameterized complexity point of view. In the Partition into H problem the task is to partition vertices of a graph G into sets V 1 , V 2 , . . . , V n such that the graph H is isomorphic to the subgraph of G induced by each set V i for i = 1, 2, . . . , n. The pattern graph H is fixed.For the parametrization we consider three distinct structural parameters of the graph Gnamely 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. Finally, for the parametrization by the modular-width we derive an FPT algorithm for every prime graph H.