Minimum vertex degree threshold for loose Hamilton cycles in 3-uniform hypergraphs

Abstract

We show that for sufficiently large $n$, every 3-uniform hypergraph on $n$ vertices with minimum vertex degree at least $\left(\genfrac{}{}{0ex}{}{n-1}{2}\right)-\left(\genfrac{}{}{0ex}{}{\lfloor \frac{3}{4}n\rfloor }{2}\right)+c$, where $c=2$ if $n\in 4\mathbb{N}$ and $c=1$ if $n\in 2\mathbb{N}\setminus 4\mathbb{N}$, contains a loose Hamilton cycle. This degree condition is best possible and improves on the work of Buß, Hàn and Schacht who proved the corresponding asymptotical result.

23 pages, 1 figure, Accepted for publication in JCTB

References in corpus (2)

• Minimum vertex degree conditions for loose Hamilton cycles in $3$-uniform hypergraphs
• Hamilton cycles in graphs and hypergraphs: an extremal perspective

Cited by in corpus (4)

• Minimum vertex degree condition for tight Hamiltonian cycles in 3-uniform hypergraphs
• Minimum vertex degree thresholds for tiling complete 3-partite 3-graphs
• Loose Hamiltonian cycles forced by large $(k-2)$-degree - approximate version
• On the Hamiltonicity of triple systems with high minimum degree