Codegree Turán Density of Tight Cycles in Hypergraphs
Published:Dec 28, 2025 17:19
•1 min read
•ArXiv
Analysis
This paper investigates the codegree Turán density of tight cycles in k-uniform hypergraphs. It improves upon existing bounds and provides exact values for certain cases, contributing to the understanding of extremal hypergraph theory. The results have implications for the structure of hypergraphs with high minimum codegree and answer open questions in the field.
Key Takeaways
- •Improved bounds and exact values for the codegree Turán density of tight cycles.
- •Generalization of a previous result for 3-uniform tight cycles.
- •Answers to open questions regarding the tightness of constructions.
- •Determination of the codegree Turán density for tight cycles with a removed edge for a new set of integers.
Reference
“The paper establishes improved upper and lower bounds on γ(C_ℓ^k) for general ℓ not divisible by k. It also determines the exact value of γ(C_ℓ^k) for integers ℓ not divisible by k in a set of (natural) density at least φ(k)/k.”