Hamilton cycles in quasirandom hypergraphs1. Issue 2 (26th February 2016) - Lenz, John; Mubayi, Dhruv; Mycroft, Richard
Abstract: We show that, for a natural notion of quasirandomness in k ‐uniform hypergraphs, any quasirandom k ‐uniform hypergraph on n vertices with constant edge density and minimum vertex degree Ω( n k ‐1 ) contains a loose Hamilton cycle. We also give a construction to show that a k ‐uniform hypergraph satisfying these conditions need not contain a Hamilton ℓ ‐cycle if k – ℓ divides k . The remaining values of ℓ form an interesting open question. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 49, 363–378, 2016