{"paper":{"title":"The Multiple-orientability Thresholds for Random Hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Konstantinos Panagiotou, Megha Khosla, Nikolaos Fountoulakis","submitted_at":"2013-09-26T09:36:19Z","abstract_excerpt":"A $k$-uniform hypergraph $H = (V, E)$ is called $\\ell$-orientable, if there is an assignment of each edge $e\\in E$ to one of its vertices $v\\in e$ such that no vertex is assigned more than $\\ell$ edges. Let $H_{n,m,k}$ be a hypergraph, drawn uniformly at random from the set of all $k$-uniform hypergraphs with $n$ vertices and $m$ edges. In this paper we establish the threshold for the $\\ell$-orientability of $H_{n,m,k}$ for all $k\\ge 3$ and $\\ell \\ge 2$, i.e., we determine a critical quantity $c_{k, \\ell}^*$ such that with probability $1-o(1)$ the graph $H_{n,cn,k}$ has an $\\ell$-orientation i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.6772","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":""},"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"}