| Abstract: | For positive integers r>?, an r‐uniform hypergraph is called an ?‐cycle if there exists a cyclic ordering of its vertices such that each of its edges consists of r consecutive vertices, and such that every pair of consecutive edges (in the natural ordering of the edges) intersect in precisely ? vertices; such cycles are said to be linear when ?=1, and nonlinear when ?>1. We determine the sharp threshold for nonlinear Hamiltonian cycles and show that for all r>?>1, the threshold  for the appearance of a Hamiltonian ?‐cycle in the random r‐uniform hypergraph on n vertices is sharp and given by  for an explicitly specified function λ. This resolves several questions raised by Dudek and Frieze in 2011.10 |
