An Andrásfai–Erdős–Sós type theorem for F3,3 in the ℓ2-norm

Let F 3, 3 be the 3-uniform hypergraph on six vertices with edge set 123, 145, 146, 156, 245, 246, 256, 345, 346, 356. In this note, we establish an Andrásfai–Erdős–Sós type stability theorem for F 3, 3 in the ℓ 2 -norm: There exists a positive constant ξ such that for all sufficiently large n, every F 3, 3 -free 3-uniform hypergraph on n vertices with minimum ℓ 2 -norm degree at least (5 / 4 − ξ) n 3 must be bipartite. This strengthens a result of Balogh, Clemen, and Lidický 3.