{"paper":{"title":"Odd Ramsey numbers of multipartite graphs and hypergraphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Coy Schwieder, Emily Heath, Nicholas Crawford, Owen Henderschedt, Shira Zerbib","submitted_at":"2025-07-25T17:42:23Z","abstract_excerpt":"Given a hypergraph $G$ and a subhypergraph $H$ of $G$, the \\emph{odd Ramsey number} $r_{odd}(G,H)$ is the minimum number of colors needed to edge-color $G$ so that every copy of $H$ intersects some color class in an odd number of edges. Generalizing a result of \\cite{BHZ} in two different ways, in this paper we prove $r_{odd} \\left(K_{n,n}, K_{2,t} \\right)=\\frac{n}{t} + o(n)$ for all $t\\geq 2$, and $r_{odd} \\left(\\mathcal{K}^{(k)}_{n,\\dots,n}, \\mathcal{K}_{1,\\dots,1,2,2} \\right) = \\frac{n}{2} + o(n)$ for all $k\\geq 2$. The latter is the first result studying odd Ramsey numbers for hypergraphs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.19456","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/2507.19456/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"}