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 that 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. In this paper, we sharpen the upper bound to be best possible up to a constant factor. We prove that if $p > C \sqrt{\log n} /n $ for some large constant $C$, then every maximum $F_5$-free subhypergraph of $G^3(n, p)$ is tripartite with high probability.
@article{10_37236_11328,
author = {Igor Araujo and J\'ozsef Balogh and Haoran Luo},
title = {On the maximum {\(F_5\)-free} subhypergraphs of a random hypergraph},
journal = {The electronic journal of combinatorics},
year = {2023},
volume = {30},
number = {4},
doi = {10.37236/11328},
zbl = {1532.05121},
url = {http://geodesic.mathdoc.fr/articles/10.37236/11328/}
}
TY - JOUR
AU - Igor Araujo
AU - József Balogh
AU - Haoran Luo
TI - On the maximum \(F_5\)-free subhypergraphs of a random hypergraph
JO - The electronic journal of combinatorics
PY - 2023
VL - 30
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/11328/
DO - 10.37236/11328
ID - 10_37236_11328
ER -
%0 Journal Article
%A Igor Araujo
%A József Balogh
%A Haoran Luo
%T On the maximum \(F_5\)-free subhypergraphs of a random hypergraph
%J The electronic journal of combinatorics
%D 2023
%V 30
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/11328/
%R 10.37236/11328
%F 10_37236_11328
Igor Araujo; József Balogh; Haoran Luo. On the maximum \(F_5\)-free subhypergraphs of a random hypergraph. The electronic journal of combinatorics, Tome 30 (2023) no. 4. doi: 10.37236/11328
