{"paper":{"title":"A directed Andr\\'asfai-Erd\\H{o}s-S\\'os theorem and chromatic profiles of oriented cycles","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Yisai Xue","submitted_at":"2025-09-09T13:58:07Z","abstract_excerpt":"The chromatic profile of a digraph $H$, denoted by $\\delta_{\\chi}^{+}(H,k)$, is the infimum $d$ such that any $H$-free digraph $D$ on $n$ vertices with minimum out-degree $\\delta^{+}(D) \\ge dn$ must be $k$-colorable. We determine the exact chromatic profile for several fundamental classes of digraphs. Our main result is a directed analogue of the Andr\\'asfai-Erd\\H{o}s-S\\'os theorem, stating that $\\delta_\\chi^{+}(T_r, r-1)=\\frac{3 r-7}{3 r-4}$, where $T_r$ is the transitive tournament on $r$ vertices. We then determine the chromatic profile for directed odd cycles, showing that $\\delta^+_\\chi(\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.07760","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/2509.07760/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"}