{"paper":{"title":"The size of the giant component in random hypergraphs: a short proof","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CO","authors_text":"Christoph Koch, Mihyun Kang, Oliver Cooley","submitted_at":"2018-03-07T18:36:42Z","abstract_excerpt":"We consider connected components in $k$-uniform hypergraphs for the following notion of connectedness: given integers $k\\ge 2$ and $1\\le j \\le k-1$, two $j$-sets (of vertices) lie in the same $j$-component if there is a sequence of edges from one to the other such that consecutive edges intersect in at least $j$ vertices.\n  We prove that certain collections of $j$-sets constructed during a breadth-first search process on $j$-components in a random $k$-uniform hypergraph are reasonably regularly distributed with high probability. We use this property to provide a short proof of the asymptotic s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.02809","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"}