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

Abstract

We show that every 3-uniform hypergraph with $n$ vertices and minimum vertex degree at least $(5/9+o(1))\left(\genfrac{}{}{0ex}{}{n}{2}\right)$ contains a tight Hamiltonian cycle. Known lower bound constructions show that this degree condition is asymptotically optimal.

38 pages, second version addresses changes arising from the referee reports

References in corpus (2)

• Minimum vertex degree conditions for loose Hamilton cycles in $3$-uniform hypergraphs
• On the Hamiltonicity of triple systems with high minimum degree

Cited by in corpus (10)

• Hamiltonicity in randomly perturbed hypergraphs
• On Hamiltonian cycles in hypergraphs with dense link graphs
• Counting Hamilton cycles in Dirac hypergraphs
• Minimum pair degree condition for tight Hamiltonian cycles in $4$-uniform hypergraphs
• Squares of Hamiltonian cycles in 3-uniform hypergraphs
• Resilience for tight Hamiltonicity
• Hamiltonicity in Cherry-quasirandom 3-graphs
• Cover 3-uniform hypergraphs by vertex-disjoint tight paths
• Transversal Hamilton cycle in hypergraph systems
• Large $Y_{k,b}$-tilings and Hamilton $\ell$-cycles in $k$-uniform hypergraphs