Minimum degree conditions for Hamilton $l$-cycles in $k$-uniform hypergraphs

Abstract

We show that for $\hat{I}\cdot >0$ and sufficiently large $n$, every 5-graph on $n$ vertices with $\hat{I}{´}_2(H)\ge (91/216+\hat{I}\cdot )\left(\genfrac{}{}{0ex}{}{n}{3}\right)$ contains a Hamilton 2-cycle. This minimum 2-degree condition is asymptotically best possible. Moreover, we give some related results on Hamilton $\ell$-cycles with $d$-degree for $\ell \le d\le k-1$ and $1\le \ell <k/2$.