## Abstract

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 (Formula present) then with high probability there exists a maximum F_{5}-free subhy-pergraph 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 (Formula present) for some large constant C, then every maximum F_{5}-free subhypergraph of G^{3}(n, p) is tripartite with high probability.

Original language | English (US) |
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Article number | P4.22 |

Journal | Electronic Journal of Combinatorics |

Volume | 30 |

Issue number | 4 |

DOIs | |

State | Published - 2023 |

## ASJC Scopus subject areas

- Theoretical Computer Science
- Geometry and Topology
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics
- Applied Mathematics

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