Loose Hamiltonian cycles forced by large $(k-2)$-degree - sharp version

Abstract

We prove for all $k\ge 4$ and $1\le \ell <k/2$ the sharp minimum $(k-2)$-degree bound for a $k$-uniform hypergraph $\mathcal{H}$ on $n$ vertices to contain a Hamiltonian $\ell$-cycle if $k-\ell$ divides $n$ and $n$ is sufficiently large. This extends a result of Han and Zhao for $3$-uniform hypegraphs.

14 pages, second version addresses changes arising from the referee reports