Mingyuan Rong, The codegree Turán density of tight cycles
The codegree Turán density γ(F) of a k-uniform hypergraph F is the smallest γ ≥ 0 with the following property: if every set of k−1 vertices in an n-vertex k-uniform hypergraph H lies in at least (γ+o(1))n edges, then H contains a copy of F for all sufficiently large n. Piga, Sanhueza-Matamala, and Schacht proved …