Loose Hamilton cycles in hypergraphs

We prove that any k-uniform hypergraph on n vertices with minimum degree at least n 2(k−1) + o(n) contains a loose Hamilton cycle. The proof strategy is similar to that used by K¨uhn and Osthus for the 3-uniform case. Though some additional difficulties arise in the k-uniform case, our argument here is considerably simplified by applying the recent hypergraph blow-up lemma of Keevash.

• Type: Journal
• Year: 2011
• Where: DM
• Authors: Peter Keevash, Daniela Kühn, Richard Mycroft, Deryk Osthus
• Keywords: DM 2011, Education, Hypergraph Blow-up Lemma, K-uniform Hypergraph, Loose Hamilton Cycle