Hamilton cycles in quasirandom hypergraphs

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(nk-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., 2016