Squares of Hamiltonian cycles in 3-uniform hypergraphs

Published 21 Dec 2017 in math.CO | (1712.08231v3)

Abstract: We show that every $3$-uniform hypergraph $H=(V,E)$ with $|V(H)|=n$ and minimum pair degree at least $(4/5+o(1))n$ contains a squared Hamiltonian cycle. This may be regarded as a first step towards a hypergraph version of the P\'osa-Seymour conjecture.

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