{"paper":{"title":"The asymptotic of off-diagonal online Ramsey numbers for paths","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Adva Mond, Julien Portier","submitted_at":"2023-12-27T16:26:46Z","abstract_excerpt":"We prove that for every $k\\ge 10$, the online Ramsey number for paths $P_k$ and $P_n$ satisfies $\\tilde{r}(P_k,P_n) \\geq \\frac{5}{3}n + \\frac{k}{9} - 4$, matching up to a linear term in $k$ the upper bound recently obtained by Bednarska-Bzd{\\k{e}}ga. In particular, this implies $\\lim_{n \\rightarrow \\infty} \\frac{\\tilde{r}(P_k, P_n)}{n} = \\frac{5}{3}$, whenever $10 \\le k=o(n)$, disproving a conjecture by Cyman, Dzido, Lapinskas and Lo."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.16628","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/2312.16628/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"}