Abstract
We study the emergence of loose Hamilton cycles in subgraphs of random hypergraphs. Our main result states that the minimum d-degree threshold for loose Hamiltonicity relative to the random k-uniform hypergraph Hk(n, p) coincides with its dense analogue whenever p≥ n−(k-1)/2+o(1). The value of p is approximately tight for d>(k+ 1)/2. This is particularly interesting because the dense threshold itself is not known beyond the cases when d≥k-2.
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