{"paper":{"title":"Kernelization and Sparseness: the case of Dominating Set","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Daniel Lokshtanov, Fedor V. Fomin, Felix Reidl, Fernando S\\'anchez Villaamil, Marcin Pilipczuk, Markus S. Dregi, Micha{\\l} Pilipczuk, P{\\aa}l Gr{\\o}n{\\aa}s Drange, Saket Saurabh, Sebastian Siebertz, Somnath Sikdar, Stephan Kreutzer","submitted_at":"2014-11-17T17:58:59Z","abstract_excerpt":"We prove that for every positive integer $r$ and for every graph class $\\mathcal G$ of bounded expansion, the $r$-Dominating Set problem admits a linear kernel on graphs from $\\mathcal G$. Moreover, when $\\mathcal G$ is only assumed to be nowhere dense, then we give an almost linear kernel on $\\mathcal G$ for the classic Dominating Set problem, i.e., for the case $r=1$. These results generalize a line of previous research on finding linear kernels for Dominating Set and $r$-Dominating Set. However, the approach taken in this work, which is based on the theory of sparse graphs, is radically dif"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.4575","kind":"arxiv","version":2},"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"}