Minimum pair-degee for tight Hamiltonian cycles in 4-uniform hypergraphs

Abstract

We show that every 4-uniform hypergraph with n vertices and minimum pair-degree at least (5/9+o(1))n^2/2 contains a tight Hamiltonian cycle. This degree condition is asymptotically optimal. In the proof we use a variant of the absorbing method and ideas from the proof of the optimal minimum vertex degree condition for tight Hamiltonian cycles in 3-uniform hypergraphs that was obtained in a previous work by Reiher, Rödl, Ruciński, Schacht, and Szemerédi.