Loose Hamilton cycles in 3-uniform hypergraphs of high minimum degree

Authors:
Daniela Kühn;Deryk Osthus
Affiliations:
School of Mathematics, Birmingham University, Edgbaston, Birmingham B15 2TT, UK;School of Mathematics, Birmingham University, Edgbaston, Birmingham B15 2TT, UK
Venue:
Journal of Combinatorial Theory Series B
Year:
2006

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Abstract

We say that a 3-uniform hypergraph has a Hamilton cycle if there is a cyclic ordering of its vertices such that every pair of consecutive vertices lies in a hyperedge which consists of three consecutive vertices. Also, let C"4 denote the 3-uniform hypergraph on 4 vertices which contains 2 edges. We prove that for every @e0 there is an n"0 such that for every n=n"0 the following holds: Every 3-uniform hypergraph on n vertices whose minimum degree is at least n/4+@en contains a Hamilton cycle. Moreover, it also contains a perfect C"4-packing. Both these results are best possible up to the error term @en.