We show that for sufficiently large $n$, every 3-uniform hypergraph on $n$ vertices with minimum vertex degree at least $\binom{ n-1}2 - \binom{ \lfloor\frac34 n\rfloor}2 + c$, 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 Bu\ss, H\`an and Schacht who proved the corresponding asymptotical result.
Categories: math.CO