Kernelization is a central technique used in parameterized algorithms, and in other approaches for coping with NP-hard problems. In this paper, we introduce a new method which allows us to show that many problems do not have polynomial size kernels under reasonable complexity-theoretic assumptions. These problems include k-Path, k-Cycle, k-Exact Cycle, k-Short Cheap Tour, k-Graph Minor Order Test, k-Cutwidth, k-Search Number, k-Pathwidth, k-Treewidth, k-Branchwidth, and several optimization problems parameterized by treewidth or cliquewidth.
35th International Colloquium on Automata, Languages and Programming (ICALP 2008). Automata, Languages and Programming (Reykjavik, Iceland 7-11 July, 2008) p. 563-574