{"paper":{"title":"On the rainbow matching conjecture for 3-uniform hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hongliang Lu, Jie Ma, Jun Gao, Xingxing Yu","submitted_at":"2020-11-29T13:03:33Z","abstract_excerpt":"Aharoni and Howard, and, independently, Huang, Loh, and Sudakov proposed the following rainbow version of Erd\\H{o}s matching conjecture: For positive integers $n,k,m$ with $n\\ge km$, if each of the families $F_1,\\ldots, F_m\\subseteq {[n]\\choose k}$ has size more than $\\max\\{\\binom{n}{k} - \\binom{n-m+1}{k}, \\binom{km-1}{k}\\}$, then there exist pairwise disjoint subsets $e_1,\\dots, e_m$ such that $e_i\\in F_i$ for all $i\\in [m]$. We prove that there exists an absolute constant $n_0$ such that this rainbow version holds for $k=3$ and $n\\geq n_0$. We convert this rainbow matching problem to a match"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2011.14363","kind":"arxiv","version":3},"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/2011.14363/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"}