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Graph Theory and Combinatorics Seminar: On the Maximum F_5-free Subhypergraphs of G^3(n,p)

Event Type
Seminar/Symposium
Sponsor
N/A
Location
345 AH
Date
Mar 22, 2022   1:00 pm  
Speaker
Haoran Luo (UIUC)
Contact
Sean English
Views
5
Denote by F_5 the 3-uniform hypergraph on vertex set {1,2,3,4,5} with hyperedges {123,124,345}. Balogh, Butterfield, Hu, and Lenz proved that if p > K log n/n for some large constant K, then every maximum F_5-free subhypergraph of G^3(n,p) is tripartite with high probability, and showed if p_0 = 0.1\sqrt{log n}/n, then with high probability there exists a maximum F_5-free subhypergraph of G^3(n,p_0) that is not tripartite. We sharpen the upper bound to be best possible up to a constant factor. We prove that when p > C\sqrt{log n}/n for some large constant C, every maximum F_5-free subhypergraph of G^3(n,p) is tripartite with high probability. In this talk, I will introduce the main technique we use to improve this bound.
 

This is a joint work with Igor Araujo and Jozsef Balogh.

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