Graph Theory and Combinatorics Seminar
- Event Type
- Seminar/Symposium
- Sponsor
- Department of Mathematics
- Location
- Gregory Hall 327
- Date
- Nov 5, 2024 1:00 pm
- Contact
- Peter Bradshaw
- pb38@illinois.edu
- Views
- 15
- Originating Calendar
- Combinatorics Research Area Calendar
Speaker: Zoltan Furedi (Renyi Institute and UIUC)
Title: A Turan type problem for triple-systems
Abstract: Let F be a triple system of 4 members consisting of three disjoint edges and the fourth one meeting each in a singleton, (F= {123, 456, 789, 147} ). We prove the following conjecture of Gyarfas (in a stronger form). If H is a 3-uniform hypergraph with n vertices, F-free, and n is sufficiently large then |H| \leq (n-2)^2. Here equality holds only if H consists of all the {n-1 \choose 2} + {n-2 \choose 2} triples meeting two given vertices.