## Graph Theory and Combinatorics Seminar

- Event Type
- Seminar/Symposium
- Sponsor
- Department of Mathematics
- Location
- 111 Gregory Hall
- Date
- Sep 19, 2023 1:00 pm
- Contact
- Peter Bradshaw
- pb38@illinois.edu
- Phone
- 217-898-4426
- Views
- 3
- Originating Calendar
- Combinatorics Research Area Calendar
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.