Turán density of tight cycles minus one edge in the ℓ₂-norm

2025/07/01 by Bodnár, Levente, Deng, Jinghua, Hou, Jianfeng +2
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2507.00812

Abstract

The 3-uniform tight ℓ-cycle minus one edge C_ℓ^3- is the 3-graph on ℓ vertices consisting of ℓ-1 consecutive triples in the cyclic order. We show that for every integer ℓ ≥ 5 satisfying ℓ\not≡ 0\pmod3, every C_ℓ^3--free 3-graph whose ℓ₂-norm, that is, the sum of codegree squares, is close to the maximum must be structurally close to the iterative blowup of a single triple. This confirms a conjecture of Balogh--Clemen--Lidický~[Surveys in combinatorics 2022, 21-63] in a stronger form.

Citations

• The Turán density of the tight 5-cycle minus one edge
• Phase transition of degenerate Turán problems in p-norms
• Nondegenerate Turán problems under (t,p)-norms
• Turán density of long tight cycle minus one hyperedge
• Flag Algebras: A First Glance
• Hypergraphs do jump
• A Turán Type Problem Concerning the Powers of the Degrees of a Graph (revised)
• On extremal problems of graphs and generalized graphs

Related

• The Turán density of the tight 5-cycle minus one edge
• The Turán density of short tight cycles
• The codegree Turán density of 3-uniform tight cycles
• The Turán density of tight cycles in three-uniform hypergraphs
• The codegree Turán density of tight cycles minus one edge