Loose Hamiltonian cycles forced by large $(k-2)$-degree - approximate version

Abstract

We prove that for all $k\ge 4$ and $1\le \ell <k/2$, every $k$-uniform hypergraph $\mathcal{H}$ on $n$ vertices with ${\delta }_{k-2}(\mathcal{H})\ge \left(\frac{4(k-\ell )-1}{4(k-\ell {)}^2}+o(1)\right)\left(\genfrac{}{}{0ex}{}{n}{2}\right)$ contains a Hamiltonian $\ell$-cycle if $k-\ell$ divides $n$. This degree condition is asymptotically best possible. The case $k=3$ was addressed earlier by Buß et al.

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

References in corpus (1)

• Minimum vertex degree conditions for loose Hamilton cycles in $3$-uniform hypergraphs

Cited by in corpus (1)

• A rainbow Dirac theorem for loose Hamilton cycles in hypergraphs