We show that 3-graphs on n vertices whose codegree is at least p2{3 `op1qqn can be decomposed into tight cycles and admit Euler tours, subject to the trivial necessary divisibility conditions. We also provide a construction showing that our bounds are best possible up to the op1q term. All together, our results answer in the negative some recent questions of Glock, Joos, Kühn, and Osthus.

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Given $\alpha \gt 0$ and an integer $\ell \geq 5$ , we prove that every sufficiently large $3$ -uniform hypergraph $H$ on $n$ vertices in which every two vertices are contained in at least $\alpha n$ edges contains a copy of $C_\ell ^{-}$ , a tight cycle on $\ell$ vertices minus one edge. This improves a previous result by Balogh, Clemen, and Lidický.

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