{"paper":{"title":"The $k$-in-a-tree problem for graphs of girth at least~$k$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Nicolas Trotignon, Wei Liu","submitted_at":"2013-09-05T08:52:16Z","abstract_excerpt":"For all integers $k\\geq 3$, we give an $O(n^4)$ time algorithm for the problem whose instance is a graph $G$ of girth at least $k$ together with $k$ vertices and whose question is \"Does $G$ contains an induced subgraph containing the $k$ vertices and isomorphic to a tree?\". This directly follows for $k=3$ from the three-in-a-tree algorithm of Chudnovsky and Seymour and for $k=4$ from a result of Derhy, Picouleau and Trotignon. Here we solve the problem for $k\\geq 5$. Our algorithm relies on a structural description of graphs of girth at least $k$ that do not contain an induced tree covering $k"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.1279","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"}