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Theoretical Computer Science
| Hi-index | 5.23 |
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 II, are there k vertices of G that induce a subgraph with property II? This problem has been proved NP-hard by Lewis and Yannakakis. We show that if II 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.