{"paper":{"title":"Long antipaths and anticycles in oriented graphs","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bin Chen, Hongyu Zhou, Xinmin Hou","submitted_at":"2024-01-10T15:04:02Z","abstract_excerpt":"Let $\\delta^{0}(D)$ be the minimum semi-degree of an oriented graph $D$. Jackson (1981) proved that every oriented graph $D$ with $\\delta^{0}(D)\\geq k$ contains a directed path of length $2k$ when $|V(D)|>2k+2$, and a directed Hamilton cycle when $|V(D)|\\le 2k+2$. Stein~(2020) further conjectured that every oriented graph $D$ with $\\delta^{0}(D)>k/2$ contains any orientated path of length $k$. Recently, Klimo\\u{s}ov\\'{a} and Stein (DM, 2023) introduced the minimum pseudo-semi-degree $\\tilde\\delta^0(D)$ (a slight weaker than the minimum semi-degree condition as $\\tilde\\delta^0(D)\\ge \\delta^0(D)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.05205","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2401.05205/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"}