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Let $n>k>\ell$ be positive integers. We say a $k$-uniform hypergraph$\mathcal{H}$ contains a Hamilton $(\ell,k-\ell)$-cycle if there is a partition$(L_0,R_0,L_1,R_1,\ldots,L_{t-1},R_{t-1})$ of $V(\mathcal{H})$ with$|L_i|=\ell$, $|R_i|=k-\ell$ such that $L_i\cup R_i$ and $R_i\cup L_{i+1}$(subscripts module $t$) are all edges of $\mathcal{H}$ for $i=0,1,\ldots,t-1$.In the present paper, we determine the tight minimum $\ell$-degree conditionthat guarantees the existence of a Hamilton $(\ell,k-\ell)$-cycle in every$k$-uniform $n$-vertex hypergraph for $k\geq 7$, $k/2\leq \ell\leq k-1$ andsufficiently large $n\in k\mathbb{N}$.

Minimum degree thresholds for Hamilton $(\ell,k-\ell)$-cycles in $k$-uniform hypergraphs