# An exact result for 3-graphs

@article{Frankl1984AnER, title={An exact result for 3-graphs}, author={Peter Frankl and Zolt{\'a}n F{\"u}redi}, journal={Discret. Math.}, year={1984}, volume={50}, pages={323-328} }

Abstract The aim of this paper is to prove Theorem 1 which gives a full description of families of 3-subsets in which any 4 points contain 0 or 2 members of the family.

#### Figures from this paper

#### 75 Citations

On 3-Hypergraphs with Forbidden 4-Vertex Configurations

- Mathematics, Computer Science
- SIAM J. Discret. Math.
- 2010

The proof is a rather elaborate application of Cauchy-Schwarz-type arguments presented in the framework of flag algebras by re-proving a few known tight results about hypergraph Turan densities and significantly improving numerical bounds for several problems for which the exact value is not known yet. Expand

Tur an problems on

- Mathematics
- 2014

A non-uniform hypergraph H = (V;E) consists of a vertex set V and an edge set E 2 V ; the edges in E are not required to all have the same cardinality. The set of all cardinalities of edges in H is… Expand

On the Maximum Induced Density of Directed Stars and Related Problems

- Mathematics, Computer Science
- SIAM J. Discret. Math.
- 2014

It is proved that the maximum induced density of the $k$-vertex directed star in a directed graph is asymptotically attained by an iterated blow-up construction. Expand

Codegree Thresholds for Covering 3-Uniform Hypergraphs

- Computer Science, Mathematics
- SIAM J. Discret. Math.
- 2016

Given two 3-uniform hypergraphs F and G = (V, E), we say that G has an F-covering if we can cover V with copies of F. The minimum codegree of G is the largest integer d such that every pair of vert… Expand

On Hypergraphs with Every Four Points Spanning at Most Two Triples

- Computer Science, Mathematics
- Electron. J. Comb.
- 2003

This paper improves previous bounds of de Caen and Matthias on a triple system on an n element set by finding a set of four points containing at least three triples of F. Expand

A PROBLEM OF ERD ý OS AND S ´ OS ON 3-GRAPHS

- Mathematics
- 2014

We show that for every " > 0 there exist � > 0 and n0 2 N such that every 3-uniform hypergraph on nn0 vertices with the property that every k-vertex subset, where k � �n, induces at least 1 + " �… Expand

On the density of 2-colorable 3-graphs in which any four points span at most two edges

- Mathematics
- 2009

Let ex(2) (n, kappa(-)(4)) be the maximum number of edges in a 2-colorable kappa(-)(4)-free 3-graph (where kappa(-)(4) ={123,124,134}). The 2-chromatic Turan density of kappa(-)(4) is pi(2)(kappa(-… Expand

The Turan Density of Triple Systems Is Not Principal

- Computer Science, Mathematics
- J. Comb. Theory, Ser. A
- 2002

An example is given, which shows that the conjecture that the Erdos-Stone-Simonovits Theorem implies that the Turan density of a family of graphs is the minimum of theTuran densities of the individual graphs from the family is true. Expand

Constructions of non-principal families in extremal hypergraph theory

- Computer Science, Mathematics
- Discret. Math.
- 2008

It is observed that the demonstrated non-principality phenomenon holds also with respect to the Ramsey-Turan density as well. Expand

3-uniform Hypergraphs: Modular Decomposition and Realization by Tournaments

- Computer Science, Mathematics
- Contributions Discret. Math.
- 2020

The 3-uniform hypergraphs that admit realizations by using a suitable modular decomposition are characterized. Expand

#### References

SHOWING 1-6 OF 6 REFERENCES

Three-graphs without two triples whose symmetric difference is contained in a third

- Computer Science, Mathematics
- Discret. Math.
- 1974

The aim of this note is to prove Katona's conjecture that if a three-graph has 3n vertices and n^3+1 triples, then there are two triples whose symmetric difference is contained in a third triple. Expand

Extremal Problems for Hypergraphs

- Mathematics
- 1975

By a hypergraph we mean a pair (V,A), where V is a finite set, and A = {A1,…,Am} is a family of its different subsets. |V| means the number 1 m of elements of V; this is usually denoted simply by n.… Expand

A new generalization of the Erdős-Ko-Rado theorem

- Mathematics, Computer Science
- Comb.
- 1983

This paper shows that the Erdős-Ko-Rado theorem holds forn>n0(k) if and only ifs≧2k, and sharpens a theorem of Bollobás. Expand

On Ramsey—Turán type theorems for hypergraphs

- Mathematics, Computer Science
- Comb.
- 1982

It is shown that ifr>2 andHr is e.g. a complete graph then the minimal integer f(n;Hr, varepsilon n) = 0 is in strong contrast with the situation in caser=2. Expand

Extrernal problems for hypergraphs , Math

- Centre Tracts
- 1983

A new generalization of the Erd 6 sKoRado theorem