The Turán density of the tight 5-cycle minus one edge

2024/12/30 by Levente Bodnár, Jared León, Bodnár, Levente +5 · 4 citations
Computer Science · Mathematics · #Computability, Logic, AI Algorithms #Advanced Topology and Set Theory #Advanced Graph Theory Research

paper · pdf · doi:10.48550/arxiv.2412.21011

Abstract

Let the tight ℓ-cycle minus one edge C_ℓ^3- be the 3-graph on \1,…,ℓ\ consisting of ℓ-1 consecutive triples in the cyclic order. We show that, for every ℓ≥ 5 not divisible by 3, the Turán density of C_ℓ^3- is 1/4 and also prove some finer structure results. This proves a conjecture of Mubayi--Sudakov--Pikhurko from 2011 and extends the results of Balogh--Luo [Combinatorica 44 (2024) 949--976] who established analogous claims for all sufficiently large ℓ. Results similar to ours were independently obtained by Lidický--Mattes--Pfender [arXiv:2409.14257].

Cited by

• The codegree Turán density of tight cycles
• Odd hypergraph Mantel theorems
• Exact Turán densities in triple systems
• Turán density of tight cycles minus one edge in the ℓ₂-norm

Related

• The Turán density of short tight cycles
• Turán density of tight cycles minus one edge in the ℓ₂-norm
• Turán density of long tight cycle minus one hyperedge
• The Hypergraph Turán Densities of Tight Cycles Minus an Edge
• The codegree Turán density of tight cycles minus one edge