Speaker: Haoran Luo (UIUC)
Title: Turán density of long tight cycle minus one hyperedge
Abstract: Denote by C_ℓ^- the 3-uniform hypergraph obtained by removing one hyperedge from the tight cycle on ℓ vertices. It is conjectured that the Turán density of C_5^- is 1/4. We make progress toward this conjecture by proving that the Turán density of C_ℓ^- is 1/4, for every sufficiently large ℓ not divisible by 3. One of the main ingredients of our proof is a forbidden-subhypergraph characterization of the hypergraphs, for which there exists a tournament on the same vertex set such that every hyperedge is a cyclic triangle in this tournament.
This is joint work with József Balogh.