Abstract: The Turán density of an r-uniform hypergraph H is the limit of the maximum density of an n-vertex r-uniform hypergraph not containing a copy of H, as n tends to infinity.
Denote by Ct the 3-uniform tight cycle on t vertices. Mubayi and Rödl (2002) gave an `iterated blow-up' construction showing that the Turán density of C5 is at least 2\sqrt{3}-3, and this bound is conjectured to be tight. Their construction also does not contain any Ct for larger t not divisible by 3, which suggests that it might be an extremal construction for these hypergraphs as well. We show that, for large t not divisible by 3, the Turán density of Ct is, indeed, 2\sqrt{3}-3.
This is joint work with Nina Kamčev and Alexey Pokrovskiy.
