{"paper":{"title":"A general approach to transversal versions of Dirac-type theorems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alp M\\\"uyesser, Amedeo Sgueglia, Fabian Hamann, Olaf Parczyk, Pranshu Gupta","submitted_at":"2022-09-19T18:28:01Z","abstract_excerpt":"Given a collection of hypergraphs $\\textbf{H}=(H_1,\\ldots,H_m)$ with the same vertex set, an $m$-edge graph $F\\subset \\cup_{i\\in [m]}H_i$ is a transversal if there is a bijection $\\phi:E(F)\\to [m]$ such that $e\\in E(H_{\\phi(e)})$ for each $e\\in E(F)$. How large does the minimum degree of each $H_i$ need to be so that $\\textbf{H}$ necessarily contains a copy of $F$ that is a transversal? Each $H_i$ in the collection could be the same hypergraph, hence the minimum degree of each $H_i$ needs to be large enough to ensure that $F\\subseteq H_i$. Since its general introduction by Joos and Kim [Bull. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.09289","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/2209.09289/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"}