{"paper":{"title":"The threshold for the asymmetric vertex-Ramsey property in randomly perturbed graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Asier Calbet R\\'ipodas, Joseph Hyde, Victor Falgas-Ravry","submitted_at":"2026-06-29T16:47:45Z","abstract_excerpt":"For $r \\geq 2$ and graphs $H_1, \\ldots, H_r, G$, we say that $G$ is $(H_1, \\ldots, H_r)$ vertex-Ramsey, or $(H_1, \\ldots, H_r)_v$-Ramsey, if whenever we colour the vertices of $G$ with colours from the set $[r]=\\{1,2, \\ldots, r\\}$ there exists $j \\in [r]$ such that some copy of $H_j$ in $G$ is monochromatic in colour $j$. Given any fixed collection of graphs $H_1, \\ldots, H_r$, Luczak, Ruci\\'{n}ski and Voigt and Kreuter determined in the 1990s the threshold edge probability $p$ at which the binomial random graph $G(n,p)$ becomes $(H_1, \\ldots, H_r)_v$-Ramsey. More recently, Das, Morris and Tre"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.30548","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/2606.30548/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"}