  For $1\le d\le \ell< k$, we give a new lower bound for the minimum $d$-degree
threshold that guarantees a Hamilton $\ell$-cycle in $k$-uniform hypergraphs.
When $k\ge 4$ and $d< \ell=k-1$, this bound is larger than the conjectured
minimum $d$-degree threshold for perfect matchings and thus disproves a
well-known conjecture of R\"odl and Ruci\'nski. Our (simple) construction
generalizes a construction of Katona and Kierstead and the space barrier for
Hamilton cycles.
