A note on hypergraph extensions of Mantel's theorem

2025/05/16 by Jie Ma, Ma, Jie, Tianming Zhu +1 · 2 citations
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #Markov Chains and Monte Carlo Methods #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2505.11373

openalex publication_date 2025/05/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Chao and Yu introduced an entropy method for hypergraph Turán problems, and used it to show that the family of \lfloor k/2\rfloor k-uniform tents have Turán density k!/k^k. Il'kovič and Yan improved this by reducing to a subfamily of \lceil k/e\rceil tents. In this note, enhancing Il'kovič-Yan's result, we give a significantly shorter entropy proof, with optimal bounds within this framework.

Citations

• An improved hypergraph Mantel's Theorem
• On a hypergraph Mantel theorem

Cited by

• Entropy methods in combinatorics
• Odd hypergraph Mantel theorems

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