Parameterized complexity of finding subgraphs with hereditary properties

Subhash Khot, Venkatesh Raman

Research output: Contribution to journalConference articlepeer-review


We consider the parameterized complexity of the following problem under the framework introduced by Downey and Fellows: Given a graph G, an integer parameter k and a nontrivial hereditary property Π, are there k vertices of G that induce a subgraph with property Π? This problem has been proved NP-hard by Lewis and Yannakakis. We show that if Π includes all trivial graphs but not all complete graphs or vice versa, then the problem is complete for the parameterized class W[1] and is fixed parameter tractable otherwise. Our proofs of both the tractability and hardness involve nontrivial use of the theory of Ramsey numbers.

Original languageEnglish (US)
Pages (from-to)997-1008
Number of pages12
JournalTheoretical Computer Science
Issue number2
StatePublished - Oct 30 2002
EventComputing and Combinatorics (COCOON 2000) - Sydney, NSW, Australia
Duration: Jul 1 2000Jul 1 2000


  • Hereditary properties
  • Parameterized complexity
  • Ramsey numbers

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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