{"paper":{"title":"The Parameterized Complexity of Graph Cyclability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.DM","cs.DS"],"primary_cat":"math.CO","authors_text":"Dimitrios M. Thilikos, Marcin Kami\\'nski, Petr A. Golovach, Spyridon Maniatis","submitted_at":"2014-12-12T11:43:40Z","abstract_excerpt":"The cyclability of a graph is the maximum integer $k$ for which every $k$ vertices lie on a cycle. The algorithmic version of the problem, given a graph $G$ and a non-negative integer $k,$ decide whether the cyclability of $G$ is at least $k,$ is {\\sf NP}-hard. We study the parametrized complexity of this problem. We prove that this problem, parameterized by $k,$ is ${\\sf co\\mbox{-}W[1]}$-hard and that its does not admit a polynomial kernel on planar graphs, unless ${\\sf NP}\\subseteq{\\sf co}\\mbox{-}{\\sf NP}/{\\sf poly}$. On the positive side, we give an {\\sf FPT} algorithm for planar graphs tha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.3955","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"}