Properly colored Hamilton cycles in Dirac-type hypergraphs (Q2692184)

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