Title: Co-degree thresholds for extremal problems on 3-uniform hypergraphs
Abstract: There are various different notions measuring extremality of hypergraphs. We compare the recently introduced notion of the codegree squared extremal function with the Turán function, the minimum codegree threshold and the uniform Turán density.
The codegree squared sum co_2(G) of a 3-uniform hypergraph G is defined to be the sum of codegrees squared d(x,y)^2 over all pairs of vertices x,y. In other words, this is the square of the L2-norm of the codegree vector. We are interested in how large co_2(G) can be if we require G to be H-free for some 3-uniform hypergraph H. This maximum value of co_2(G) over all H-free n-vertex 3-uniform hypergraphs G is called the codegree squared extremal function, which we denote by exco_2(n,H).
We systemically study the extremal codegree squared sum of various 3-uniform hypergraphs using various proof techniques. Some of our proofs rely on the flag algebra method while others use more classical tools such as the stability method.
Joint work with Felix Clemen and Bernard Lidický.
