We prove that any $3$-uniform hypergraph whose minimum vertex degree is at least $\left(\frac{ 5}{ 9} + o(1) \right)\binom{ n}{ 2}$ 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, B\"ottcher, Cooley and Mycroft.
Categories: math.CO