{"paper":{"title":"On Weak Hamiltonicity of a Random Hypergraph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CO","authors_text":"Daniel Poole","submitted_at":"2014-10-27T22:28:50Z","abstract_excerpt":"A {\\it weak (Berge) cycle} is an alternating sequence of vertices and (hyper)edges $C=(v_0, e_1, v_1, ..., v_{\\ell-1}, e_\\ell, v_{\\ell}=v_0)$ such that the vertices $v_0, ..., v_{\\ell-1}$ are distinct with $v_k, v_{k+1} \\in e_{k}$ for each $k$, but the edges $e_1, ..., e_\\ell$ are not necessarily distinct. We prove that the main barrier to the random $d$-uniform hypergraph $H_d(n,p),$ where each of the potential edges of cardinality $d$ is present with probability $p$, developing a weak Hamilton cycle is the presence of isolated vertices. In particular, for $d \\geq 3$ fixed and $p=(d-1)! \\frac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.7446","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"}