Towards Pósa's Conjecture for $3$-graphs

Debmalya Bandyopadhyay, Allan Lo, Richard Mycroft

We prove that every $3$-graph $H$ on $n$ vertices with minimum codegree ${\delta }_2(H)\ge 7n/9+o(n)$ contains the square of a tight Hamilton cycle. This strengthens a theorem of Beden…