Parameterized complexity of the induced subgraph problem in directed graphs

  • Authors:

  • Venkatesh Raman;Somnath Sikdar

  • Affiliations:

  • The Institute of Mathematical Sciences, C.I.T Campus, Taramani, Chennai 600113, India;The Institute of Mathematical Sciences, C.I.T Campus, Taramani, Chennai 600113, India

  • Venue:
  • Information Processing Letters
  • Year:
  • 2007

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Abstract

In this Letter, we consider the parameterized complexity of the following problem: Given a hereditary property P on digraphs, an input digraph D and a positive integer k, does D have an induced subdigraph on k vertices with property P? We completely characterize hereditary properties for which this induced subgraph problem is W[1]-complete for two classes of directed graphs: general directed graphs and oriented graphs. We also characterize those properties for which the induced subgraph problem is W[1]-complete for general directed graphs but fixed parameter tractable for oriented graphs. These results are among the very few parameterized complexity results on directed graphs.