{"paper":{"title":"On the supersaturation of oriented Tur\\'an problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Xuanrui Hu, Yuefang Sun","submitted_at":"2026-02-15T06:25:08Z","abstract_excerpt":"The oriented Tur\\'{a}n number of a given oriented graph $\\overrightarrow{F}$, denoted by $\\exo(n,\\overrightarrow{F})$, is the largest number of arcs in $n$-vertex $\\overrightarrow{F}$-free oriented graphs. This parameter could be seen as a natural oriented version of the classical Tur\\'{a}n number. In this paper, we study the supersaturation phenomenon for oriented Tur\\'{a}n problems, and prove oriented versions of the famous Erd\\H{o}s-Simonovits Supersaturation Theorem and Moon-Moser inequality, and supersaturation theorems for tournaments and antidirected complete bipartite graphs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.14008","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/2602.14008/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"}