Properly colored Hamilton cycles in Dirac-type hypergraphs

Abstract

We consider a robust variant of Dirac-type problems in k-uniform hypergraphs. For instance, we prove that if H is a k-uniform hypergraph with minimum codegree at least 1 2 + γ n, γ > 0, and n sufficiently large, then any edge coloring φ satisfying appropriate local constraints yields a properly colored tight Hamilton cycle in H. Similar results for loose cycles are also shown.