Tight Hamiltonicity from dense links of triples

Abstract

We show that for all $k\ge 4$, $\epsilon >0$, and $n$ sufficiently large, every $k$-uniform hypergraph on $n$ vertices in which each set of $k-3$ vertices is contained in at least $(5/8+\epsilon )\left(\genfrac{}{}{0ex}{}{n}{3}\right)$ edges contains a tight Hamilton cycle. This is asymptotically best possible.

arXiv comment20 pages, major revision