A dirac-type theorem for berge cycles in random hypergraphs

Enthalten in
The electronic journal of combinatorics 
Volume
27
Issue
3
Start Page
1
End Page
23
Article Number
3.39
Citation
Electronic Journal of Combinatorics 3 (27): 3.39, 1-23 (2020)
Publisher DOI
10.37236/8611
Scopus ID
2-s2.0-85090514381
Publisher
EMIS ELibEMS
A 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.
DDC Class
510: Mathematik
More Funding Information
YP was supported by DFG grant PE 2299/1-1.