Parameterized complexity of the induced subgraph problem in directed graphs

In this paper, 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. Key words: Parameterized complexity, directed graphs, induced subgraph, hereditary properties.

• Type: Journal
• Year: 2007
• Where: IPL
• Authors: Venkatesh Raman, Somnath Sikdar
• Keywords: Hereditary Property, IPL 2007, Parameterized Complexity, Subgraph Problem