{"paper":{"title":"Two-round Ramsey games on random graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Patrick Morris, Wojciech Samotij, Yahav Alon","submitted_at":"2023-05-04T10:46:48Z","abstract_excerpt":"Motivated by the investigation of sharpness of thresholds for Ramsey properties in random graphs, Friedgut, Kohayakawa, R\\\"odl, Ruci\\'nski and Tetali introduced two variants of a single-player game whose goal is to colour the edges of a~random graph, in an online fashion, so as not to create a monochromatic triangle. In the two-round variant of the game, the player is first asked to find a triangle-free colouring of the edges of a random graph $G_1$ and then extend this colouring to a triangle-free colouring of the union of $G_1$ and another (independent) random graph $G_2$, which is disclosed"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.02725","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/2305.02725/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"}