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Loose Hamilton cycles in hypergraphs. (English) Zbl 1226.05187

Summary: We prove that any \(k\)-uniform hypergraph on \(n\) vertices with minimum degree at least \(\frac{n}{2(k-1)} + o(n)\) contains a loose Hamilton cycle. The proof strategy is similar to that used by Kühn and Osthus for the 3-uniform case. Though some additional difficulties arise in the \(k\)-uniform case, our argument here is considerably simplified by applying the recent hypergraph blow-up lemma of Keevash.

MSC:

05C65 Hypergraphs
05C45 Eulerian and Hamiltonian graphs
05C38 Paths and cycles
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