{"paper":{"title":"Transversals of Longest Paths","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Cristina G. Fernandes, Juan Guti\\'errez, M\\'arcia R. Cerioli, Paloma T. Lima, Renzo G\\'omez","submitted_at":"2017-12-19T18:13:58Z","abstract_excerpt":"Let $\\lpt(G)$ be the minimum cardinality of a set of vertices that intersects all longest paths in a graph $G$. Let $\\omega(G)$ be the size of a maximum clique in $G$, and $\\tw(G)$ be the treewidth of $G$. We prove that $ \\lpt(G) \\leq \\max\\{1,\\omega(G)-2\\}$ when $G$ is a connected chordal graph; that $\\lpt(G) =1$ when $G$ is a connected bipartite permutation graph or a connected full substar graph; and that $\\lpt(G) \\leq \\tw(G)$ for any connected graph $G$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.07086","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"}