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Similarly to the classical Ramsey setting, the upper bound <jats:italic>p<\/jats:italic><jats:sub><jats:italic>\u20d7H<\/jats:italic><\/jats:sub> \u2a7d <jats:italic>Cn<\/jats:italic><jats:sup>\u22121\/<jats:italic>m<\/jats:italic><jats:sub>2<\/jats:sub>(<jats:italic>\u20d7 H<\/jats:italic>)<\/jats:sup> is known to hold for some constant <jats:italic>C<\/jats:italic> = <jats:italic>C<\/jats:italic>( <jats:italic>\u20d7 H<\/jats:italic>), where <jats:italic>m<\/jats:italic><jats:sub>2<\/jats:sub>(<jats:italic>\u20d7<\/jats:italic><jats:italic>H<\/jats:italic>) denotes the maximum 2-density of the underlying graph <jats:italic>H<\/jats:italic> of <jats:italic>\u20d7 H<\/jats:italic>. While this upper bound is indeed the threshold for some <jats:italic>\u20d7<\/jats:italic><jats:italic>H<\/jats:italic>, this is not always the case. We obtain examples arising from rooted products of orientations of sparse graphs (such as forests, cycles and, more generally, subcubic {<jats:italic>K<\/jats:italic><jats:sub>3<\/jats:sub>, <jats:italic>K<\/jats:italic><jats:sub>3,3<\/jats:sub>}-free graphs) and arbitrarily rooted transitive triangles.<\/jats:p>","DOI":"10.1051\/ro\/2024090","type":"journal-article","created":{"date-parts":[[2024,4,24]],"date-time":"2024-04-24T08:04:24Z","timestamp":1713945864000},"page":"3607-3619","source":"Crossref","is-referenced-by-count":0,"title":["Directed graphs with lower orientation Ramsey thresholds"],"prefix":"10.1051","volume":"58","author":[{"given":"Gabriel Ferreira","family":"Barros","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bruno Pasqualotto","family":"Cavalar","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7841-157X","authenticated-orcid":false,"given":"Yoshiharu","family":"Kohayakawa","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9722-1819","authenticated-orcid":false,"given":"Guilherme Oliveira","family":"Mota","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3158-4523","authenticated-orcid":false,"given":"T\u00e1ssio","family":"Naia","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"250","published-online":{"date-parts":[[2024,9,9]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","first-page":"669","DOI":"10.1090\/S0894-0347-2014-00816-X","volume":"28","author":"Balogh","year":"2015","journal-title":"J. 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