{"paper":{"title":"Detecting induced subgraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Benjamin L\\'ev\\^eque, David Y. Lin, Fr\\'ed\\'eric Maffray, Nicolas Trotignon","submitted_at":"2013-09-04T10:51:08Z","abstract_excerpt":"An \\emph{s-graph} is a graph with two kinds of edges: \\emph{subdivisible} edges and \\emph{real} edges. A \\emph{realisation} of an s-graph $B$ is any graph obtained by subdividing subdivisible edges of $B$ into paths of arbitrary length (at least one). Given an s-graph $B$, we study the decision problem $\\Pi_B$ whose instance is a graph $G$ and question is \"Does $G$ contain a realisation of $B$ as an induced subgraph?\". For several $B$'s, the complexity of $\\Pi_B$ is known and here we give the complexity for several more. Our NP-completeness proofs for $\\Pi_B$'s rely on the NP-completeness proo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.0971","kind":"arxiv","version":1},"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"}