Loose Hamilton cycles in hypergraphs

Abstract

We prove that any k-uniform hypergraph on n vertices with minimum degree at least 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.

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References in corpus (2)

• Hamilton l-cycles in uniform hypergraphs
• Hypergraph regularity and the multidimensional Szemerédi theorem

Cited by in corpus (18)

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• Phase transition in a power-law uniform hypergraph
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• Large $Y_{k,b}$-tilings and Hamilton $\ell$-cycles in $k$-uniform hypergraphs
• Hamilton cycles in quasirandom hypergraphs
• Transversal Hamilton cycle in hypergraph systems
• Higher-dimensional counterexamples to Hamiltonicity