{"paper":{"title":"Kernelization Using Structural Parameters on Sparse Graph Classes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Felix Reidl, Fernando S\\'anchez Villaamil, Jakub Gajarsk\\'y, Jan Obdr\\v{z}\\'alek, Peter Rossmanith, Petr Hlin\\v{e}n\\'y, Sebastian Ordyniak, Somnath Sikdar","submitted_at":"2013-02-27T14:49:43Z","abstract_excerpt":"Meta-theorems for polynomial (linear) kernels have been the subject of intensive research in parameterized complexity. Heretofore, meta-theorems for linear kernels exist on graphs of bounded genus, $H$-minor-free graphs, and $H$-topological-minor-free graphs. To the best of our knowledge, no meta-theorems for polynomial kernels are known for any larger sparse graph classes; e.g., for classes of bounded expansion or for nowhere dense ones. In this paper we prove such meta-theorems for the two latter cases. More specifically, we show that graph problems that have finite integer index (FII) have "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.6863","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}