On codegree Tur\'an density of the 3-uniform tight cycle $C_{11}$

TL;DR

This paper determines the codegree Turán density of the 3-uniform tight cycle C11, completing the understanding for cycles of length at least 10, building on recent results for other cycle lengths.

Contribution

It extends existing proofs to establish the codegree Turán density for C11, filling a gap in the characterization of tight cycles of length at least 10.

Findings

Codegree Turán density of C11 is established

Completes the characterization for tight cycles of length ≥10

Builds on recent results for other cycle lengths

Abstract

Piga, Sanhueza-Matamala, and Schacht recently established that the codegree Tur\'an density of 3-uniform tight cycles $C_\ell$ is $1/3$ for $\ell\in \{10, 13, 16\}$ and for all $\ell\geq 19$. In this note, we extend their proof to determine the codegree Tur\'an density of the 3-uniform tight cycle $C_{11}$, thereby completing the picture for tight cycles of length at least 10.