{"paper":{"title":"Subcritical random hypergraphs, high-order components, and hypertrees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Mihyun Kang, Nicola Del Giudice, Oliver Cooley, Wenjie Fang","submitted_at":"2018-10-18T15:26:32Z","abstract_excerpt":"In the binomial random graph $\\mathcal{G}(n,p)$, when $p$ changes from $(1-\\varepsilon)/n$ (subcritical case) to $1/n$ and then to $(1+\\varepsilon)/n$ (supercritical case) for $\\varepsilon>0$, with high probability the order of the largest component increases smoothly from $O(\\varepsilon^{-2}\\log(\\varepsilon^3 n))$ to $\\Theta(n^{2/3})$ and then to $(1 \\pm o(1)) 2 \\varepsilon n$.\n  As a natural generalisation of random graphs and connectedness, we consider the binomial random $k$-uniform hypergraph $\\mathcal{H}^k(n,p)$ (where each $k$-tuple of vertices is present as a hyperedge with probability"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.08107","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"}