Clemens, DennisDennisClemensEhrenmüller, JuliaJuliaEhrenmüllerPerson, YuryYuryPerson2020-09-302020-09-302020-08-21Electronic Journal of Combinatorics 3 (27): 3.39, 1-23 (2020)http://hdl.handle.net/11420/7426A Hamilton Berge cycle of a hypergraph on n vertices is an alternating se-quence (v1, e1, v2, …, vn, en) of distinct vertices v1, …, vn and distinct hyperedges e1, …, en such that (Formula Presented) and (Formula Presented) for every i ∈ [n − 1]. We prove the following Dirac-type theorem about Berge cycles in the binomial random r-uniform hypergraph H(r)(n, p): for every integer r ≥ 3, every real γ > 0 and p ≥ln17rnr−1n asymptotically almost surely, (every)spanning(r−1) subgraph (Formula Presented)) with minimum vertex degree δ1(H) ≥2r−11 + γ pn contains a Hamilton Berge cycle. The minimum degree condition is asymptotically tight and the bound on p is optimal up to some polylogarithmic factor.en1077-892620203123EMIS ELibEMShttps://creativecommons.org/licenses/by-nd/4.0/MathematikJournal Article10.15480/882.294610.37236/861110.15480/882.2946Journal Article