{"paper":{"title":"Symmetric and asymmetric Ramsey properties in random hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Angelika Steger, Henning Thomas, Luca Gugelmann, Nemanja \\v{S}kori\\'c, Rajko Nenadov, Yury Person","submitted_at":"2016-10-04T11:35:19Z","abstract_excerpt":"A celebrated result of R\\\"odl and Ruci\\'nski states that for every graph $F$, which is not a forest of stars and paths of length $3$, and fixed number of colours $r\\ge 2$ there exist positive constants $c, C$ such that for $p \\leq cn^{-1/m_2(F)}$ the probability that every colouring of the edges of the random graph $G(n,p)$ contains a monochromatic copy of $F$ is $o(1)$ (the \"0-statement\"), while for $p \\geq Cn^{-1/m_2(F)}$ it is $1-o(1)$ (the \"1-statement\"). Here $m_2(F)$ denotes the $2$-density of $F$. On the other hand, the case where $F$ is a forest of stars has a coarse threshold which is"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.00935","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":""},"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"}