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One of the most famous results in the theory of random graphs establishes that the threshold for Hamiltonicity in the Erdős‐Rényi random graph Gn,p is around . Much research has been done to extend this to increasingly challenging random structures. In particular, a recent result by Frieze determined the asymptotic threshold for a loose Hamilton cycle in the random 3‐uniform hypergraph...
Let H be a 3‐uniform hypergraph with n vertices. A tight Hamilton cycle C ⊂ H is a collection of n edges for which there is an ordering of the vertices v1,…,vn such that every triple of consecutive vertices {vi,vi+1,vi+2} is an edge of C (indices are considered modulo n ). We develop new techniques which enable us to prove that under certain natural pseudo‐random conditions, almost all edges of H...
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