{"paper":{"title":"Exploring Subexponential Parameterized Complexity of Completion Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Fedor V. Fomin, Micha{\\l} Pilipczuk, P{\\aa}l Gr{\\o}n{\\aa}s Drange, Yngve Villanger","submitted_at":"2013-09-16T16:16:41Z","abstract_excerpt":"Let ${\\cal F}$ be a family of graphs. In the ${\\cal F}$-Completion problem, we are given a graph $G$ and an integer $k$ as input, and asked whether at most $k$ edges can be added to $G$ so that the resulting graph does not contain a graph from ${\\cal F}$ as an induced subgraph. It appeared recently that special cases of ${\\cal F}$-Completion, the problem of completing into a chordal graph known as Minimum Fill-in, corresponding to the case of ${\\cal F}=\\{C_4,C_5,C_6,\\ldots\\}$, and the problem of completing into a split graph, i.e., the case of ${\\cal F}=\\{C_4, 2K_2, C_5\\}$, are solvable in par"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.4022","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"}