{"paper":{"title":"Directed graphs with lower orientation Ramsey thresholds","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bruno Pasqualotto Cavalar, Gabriel Ferreira Barros, Guilherme Oliveira Mota, T\\'assio Naia, Yoshiharu Kohayakawa","submitted_at":"2022-11-13T22:27:39Z","abstract_excerpt":"We investigate the threshold $p_{\\vec H}=p_{\\vec H}(n)$ for the Ramsey-type property $G(n,p)\\to \\vec H$, where $G(n,p)$ is the binomial random graph and $G\\to\\vec H$ indicates that every orientation of the graph $G$ contains the oriented graph $\\vec H$ as a subdigraph. Similarly to the classical Ramsey setting, the upper bound $p_{\\vec H}\\leq Cn^{-1/m_2(\\vec H)}$ is known to hold for some constant $C=C(\\vec H)$, where $m_2(\\vec H)$ denotes the maximum $2$-density of the underlying graph $H$ of $\\vec H$. While this upper bound is indeed the threshold for some $\\vec H$, this is not always the ca"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.07033","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/2211.07033/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"}