{"paper":{"title":"On the random version of the Erd\\H{o}s matching conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ali Taherkhani, Meysam Alishahi","submitted_at":"2018-02-27T13:28:21Z","abstract_excerpt":"The Kneser hypergraph ${\\rm KG}^r_{n,k}$ is an $r$-uniform hypergraph with vertex set consisting of all $k$-subsets of $\\{1,\\ldots,n\\}$ and any collection of $r$ vertices forms an edge if their corresponding $k$-sets are pairwise disjoint. The random Kneser hypergraph ${\\rm KG}^r_{n,k}(p)$ is a spanning subhypergraph of ${\\rm KG}^r_{n,k}$ in which each edge of ${\\rm KG}^r_{n,k}$ is retained independently of each other with probability $p$. The independence number of random subgraphs of ${\\rm KG}^2_{n,k}$ was recently addressed in a series of works by Bollob{\\'a}s, Narayanan, and Raigorodskii ("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.09871","kind":"arxiv","version":2},"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"}