Graph Theory and Combinatorics Seminar
- Sponsor
- Department of Mathematics
- Speaker
- Haoran Luo
- Contact
- Abhishek Dhawan
- adhawan2@illinois.edu
- Views
- 4
- Originating Calendar
- Mathematics Seminar Series: Combinatorics
Speaker: Haoran Luo (UIC)
Title: A jump in the codegree Turán density of long tight cycles
Abstract: We study the codegree Turán density of C_l^r, the r-uniform hypergraph tight cycle of length l. A result of Han, Lo, and Sanhueza-Matamala states that if l is sufficiently large and r/gcd(r,l) is even, then the codegree Turán density of C_l^r is 1/2. We prove that whenever the latter assumption is not satisfied, there is a significant drop in the codegree Turán density. That is, if l is sufficiently large and r/gcd(r,l) is odd, then the codegree Turán density of C_l^r can be at most 1/3. Moreover, this bound is tight for infinitely many uniformities r and all sufficiently large l in the corresponding residue classes modulo r. Our proof makes use of a connection between Turán-type theorems and group theory.
This is a joint work with József Balogh and Maya Sankar.