Squares of Hamiltonian cycles in 3-uniform hypergraphs

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 Pósa-Seymour conjecture.

37 pages, 9 figures, third version addresses changes arising from two referee reports

References in corpus (1)

• Minimum vertex degree condition for tight Hamiltonian cycles in 3-uniform hypergraphs

Cited by in corpus (1)

• Towards a hypergraph version of the Pósa-Seymour conjecture