Minimum vertex degree threshold for loose Hamilton cycles in 3-uniform hypergraphs

We show that for sufficiently large n, every 3-uniform hypergraph on n vertices with minimum vertex degree at least ((n-1)(2)) - ((right perpendicular3/4 n left perpendicular) (2)) + c, where c = 2 if n is an element of 4N and c = 1 if n is an element of 2N \ 4N, contains a loose Hamilton cycle. This degree condition is best possible and improves on the work of BO, Han and Schacht who proved the corresponding asymptotical result. (C) 2015 Elsevier Inc. All rights reserved.