The minimum vertex degree for an almost-spanning tight cycle in a 3-uniform hypergraph

Abstract

We prove that any 3-uniform hypergraph whose minimum vertex degree is at least 59+o(1)n2 admits an almost-spanning tight cycle, that is, a tight cycle leaving o(n) vertices uncovered. The bound on the vertex degree is asymptotically best possible. Our proof uses the hypergraph regularity method, and in particular a recent version of the hypergraph regularity lemma proved by Allen, Böttcher, Cooley and Mycroft.