Minimum vertex degree condition for tight Hamiltonian cycles in   3-uniform hypergraphs
  We show that every 3-uniform hypergraph with $n$ vertices and minimum vertex degree at least $(5/9+o(1))\binom{n}2$ contains a tight Hamiltonian cycle. Known lower bound constructions show that this degree condition is asymptotically optimal. 
Christian Reiher, Vojt\v{e}ch R\"odl, Andrzej Ruci\'nski, Mathias   Schacht, Endre Szemer\'edi
math.CO