2 problems

Let $\mathbb H^{(k)}(n,d)$ denote the random $d$-regular $k$-uniform hypergraph on $n$ vertices. For integers $k>\ell\geq 2$, an $\ell$-overlapping cycle is a $k$-uniform hypergrap…

Let $\mathbb H^{(k)}(n,d)$ denote the random $d$-regular $k$-uniform hypergraph on $n$ vertices, and let a loose Hamilton cycle be a loose cycle containing all vertices. Loose Hami…