Minimum codegree threshold for Hamilton l-cycles in k-uniform hypergraphs

For $1\le \ell<k/2$, we show that for sufficiently large $n$, every $k$-uniform hypergraph on $n$ vertices with minimum codegree at least $\frac n{2 (k-\ell)}$ contains a Hamilton $\ell$-cycle. This codegree condition is best possible and improves on work of Hàn and Schacht who proved an asymptotic result.

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