Geodesic
Families of triples with high minimum degree are Hamiltonian
Discussiones Mathematicae. Graph Theory, Tome 34 (2014) no. 2, pp. 361-381.

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In this paper we show that every family of triples, that is, a 3-uniform hypergraph, with minimum degree at least (5−√5/3 + γ)n−12 contains a tight Hamiltonian cycle.
Keywords: 3-uniform hypergraph, Hamilton cycle, minimum vertex degree 
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Rödl, Vojtech; Ruciński, Andrzej. Families of triples with high minimum degree are Hamiltonian. Discussiones Mathematicae. Graph Theory, Tome 34 (2014) no. 2, pp. 361-381. http://geodesic.mathdoc.fr/item/DMGT_2014_34_2_a10/

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