• Corpus ID: 237278451

# Hypergraph Tur\'an Problems in $\ell_2$-Norm

@inproceedings{Balogh2021HypergraphTP,
title={Hypergraph Tur\'an Problems in \$\ell\_2\$-Norm},
author={J{\'o}zsef Balogh and Felix Christian Clemen and Bernard Lidick{\'y}},
year={2021}
}
• Published 23 August 2021
• Mathematics
There are various different notions measuring extremality of hypergraphs. In this survey 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 co2(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 2-norm of the codegree vector. We are interested…

## References

SHOWING 1-10 OF 69 REFERENCES

### Solving Turán’s Tetrahedron Problem for the 2-Norm

• Mathematics
• 2021
Turán’s famous tetrahedron problem is to compute the Turán density of the tetrahedron K3 4 . This is equivalent to determining the maximum `1-norm of the codegree vector of a K3 4 free n-vertex

### Exact solution of the hypergraph Turán problem for k-uniform linear paths

• Mathematics
Comb.
• 2014
The intensive use of the delta-system method is used to determine exk(n, Pℓ(k) exactly for all fixed ℓ ≥1, k≥4, and sufficiently large n, and describe the unique extremal family.

### The codegree threshold of $K_4^-$

• Mathematics
• 2021
The codegree threshold ex 2 ( n, F ) of a 3 -graph F is the minimum d = d ( n ) such that every 3 -graph on n vertices in which every pair of vertices is contained in at least d + 1 edges contains a

### A hypergraph regularity method for generalized Turán problems

The cornerstone of the approach is a quasirandom counting lemma for qu asirandom hypergraphs, which extends the standard count lemma by not only counting copies of a particular configuration but also showing that these copies are evenly distributed.

### Positive co-degree density of hypergraphs

• Mathematics
• 2022
The minimum positive co-degree of a non-empty r -graph H , denoted δ + r − 1 ( H ), is the maximum k such that if S is an ( r − 1)-set contained in a hyperedge of H , then S is contained in at least

### On the Codegree Density of Complete 3-Graphs and Related Problems

For all integers s>3, the codegree density of the complete 3-graph on s vertices K_s satisfies gamma(K_s)\geq 1-1/(s-2), which is the limit of coex(n,F)/(n-2) as n tends to infinity.

### Co-degree density of hypergraphs

• Mathematics
J. Comb. Theory, Ser. A
• 2007

### Turán densities of hypercubes

• R. Baber
• Mathematics, Computer Science
• 2012
A number of extensions to Razborov's semidefinite flag algebra method are described, including one which can be applied in a more general setting, notably to 3-uniform hypergraphs, to get a new upper bound of 0.5615 for $\pi(K_4^3)$.