# A new generalization of Mantel's theorem to k-graphs

@article{Mubayi2007ANG, title={A new generalization of Mantel's theorem to k-graphs}, author={Dhruv Mubayi and Oleg Pikhurko}, journal={J. Comb. Theory, Ser. B}, year={2007}, volume={97}, pages={669-678} }

- Published 2007 in J. Comb. Theory, Ser. B
DOI:10.1016/j.jctb.2006.11.003

Let the k-graph Fan consist of k edges that pairwise intersect exactly in one vertex x, plus one more edge intersecting each of these edges in a vertex different from x. We prove that, for n sufficiently large, the maximum number of edges in an n-vertex k-graph containing no copy of Fan is ∏ k i=1 ⌊ k ⌋, which equals the number of edges in a complete k-partite k-graph with almost equal parts. This is the only extremal example. This result is a special case of our more general theorem that… CONTINUE READING

#### From This Paper

##### Topics from this paper.

#### Citations

##### Publications citing this paper.

Showing 1-10 of 12 extracted citations

## Stability of extremal hypergraphs with applications to an edge-coloring problem

View 3 Excerpts

Highly Influenced

## Hypergraph Turán Problems

View 15 Excerpts

Highly Influenced

## Counting substructures II: Hypergraphs

View 1 Excerpt

## An analytic approach to stability

View 1 Excerpt

## Counting substructures II : triple systems

View 1 Excerpt

## Two-regular subgraphs of hypergraphs

View 1 Excerpt

#### References

##### Publications referenced by this paper.

Showing 1-10 of 21 references

## An exact Turán result for the generalized triangle

View 3 Excerpts

## A hypergraph extension of Turán's theorem

View 6 Excerpts

## Applications of the regularity lemma for uniform hypergraphs

View 2 Excerpts

## The counting lemma for regular k-uniform hypergraphs

View 2 Excerpts

## Hypergraph regularity and the multidimensional Szemerédi’s theorem

View 2 Excerpts

## On A Hypergraph Turán Problem Of Frankl

View 3 Excerpts

## The Turán Number Of The Fano Plane

View 1 Excerpt

## Triple Systems Not Containing a Fano Configuration

View 1 Excerpt

## Regularity Lemma for k-uniform hypergraphs

View 2 Excerpts

## Stability theorems for cancellative hypergraphs

View 3 Excerpts