{"paper":{"title":"On universal hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Olaf Parczyk, Samuel Hetterich, Yury Person","submitted_at":"2015-09-14T08:16:44Z","abstract_excerpt":"A hypergraph $H$ is called universal for a family $\\mathcal{F}$ of hypergraphs, if it contains every hypergraph $F \\in \\mathcal{F}$ as a copy. For the family of $r$-uniform hypergraphs with maximum vertex degree bounded by $\\Delta$ and at most $n$ vertices any universal hypergraph has to contain $\\Omega(n^{r-r/\\Delta})$ many edges. We exploit constructions of Alon and Capalbo to obtain universal $r$-uniform hypergraphs with the optimal number of edges $O(n^{r-r/\\Delta})$ when $r$ is even, $r \\mid \\Delta$ or $\\Delta=2$. Further we generalize the result of Alon and Asodi about optimal universal "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.03983","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":""},"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"}