Hamilton $\ell$-Cycles in Randomly Perturbed Hypergraphs
Hamilton $\ell$-Cycles in Randomly Perturbed Hypergraphs
We prove that for integers $2 \leqslant \ell < k$ and a small constant $c$, if a $k$-uniform hypergraph with linear minimum codegree is randomly 'perturbed' by changing non-edges to edges independently at random with probability $p \geqslant O(n^{-(k-\ell)-c})$, then with high probability the resulting $k$-uniform hypergraph contains a Hamilton …