{"paper":{"title":"Small hitting sets for longest paths and cycles","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Paul Wollan, Raphael Steiner, Sergey Norin, Stephan Thomass\\'e","submitted_at":"2025-05-13T14:52:55Z","abstract_excerpt":"Motivated by an old question of Gallai (1966) on the intersection of longest paths in a graph and the well-known conjectures of Lov\\'{a}sz (1969) and Thomassen (1978) on the maximum length of paths and cycles in vertex-transitive graphs, we present improved bounds for the parameters $\\mathrm{lpt}(G)$ and $\\mathrm{lct}(G)$, defined as the minimum size of a set of vertices in a graph $G$ hitting all longest paths (cycles, respectively). First, we show that every connected graph $G$ on $n$ vertices satisfies $\\mathrm{lpt}(G)\\le \\sqrt{8n}$, and $\\mathrm{lct}(G)\\le \\sqrt{8n}$ if $G$ is additionally"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.08634","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2505.08634/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}