Abstract

We investigate minimum vertex degree conditions for 3-uniform hypergraphs which ensure the existence of loose Hamilton cycles. A loose Hamilton cycle is a spanning cycle in which only consecutive edges intersect and these intersections consist of precisely one vertex. We prove that every 3-uniform n-vertex (n even) hypergraph H with minimum vertex degree delta(1)(H) >= (7/16 + o(1))((n)(2)) contains a loose Hamilton cycle. This bound is asymptotically best possible. (C) 2013 Elsevier Inc. All rights reserved.