• Corpus ID: 239050493

Tur\'{a}n numbers of sunflowers

@inproceedings{Bradavc2021TuranNO,
  title={Tur\'\{a\}n numbers of sunflowers},
  author={Domagoj Bradavc and Matija Buci'c and Benny Sudakov},
  year={2021}
}
A collection of distinct sets is called a sunflower if the intersection of any pair of sets equals the common intersection of all the sets. Sunflowers are fundamental objects in extremal set theory with relations and applications to many other areas of mathematics as well as theoretical computer science. A central problem in the area due to Erdős and Rado from 1960 asks for the minimum number of sets of size r needed to guarantee the existence of a sunflower of a given size. Despite a lot of… 

References

SHOWING 1-10 OF 43 REFERENCES
Improved bounds for the sunflower lemma
TLDR
This paper improves the bound on the number of sets can be improved to c w for some constant c, and proves the result for a robust notion of sunflowers, for which the bound the authors obtain is tight up to lower order terms.
SYSTEMS OF FINITE SETS HAVING A COMMON INTERSECTION
We say that a collection of finite sets has a common intersection of size t provided that the intersection of each pair of these sets is equal to the intersection of all of them and this intersection
A partition property of simplices in Euclidean space
In a series of papers, Erdos et al. [E] have investigated this property. They have shown that all Ramsey sets are spherical, that is, every Ramsey set is contained in an appropriate sphere. On the
Exact solution of some Turán-type problems
TLDR
The validity of this conjecture is established for n ⩾ n 0 ( k), in a more general framework, when the excluded configuration is a fixed sunflower.
Forbidding Just One Intersection
TLDR
It is shown that if F is a family of k-subsets of and n-set no two of which intersect in exactly l elements then for k ⩾ 2l + 2 and n sufficiently large F with equality holding if and only if F consists of all the k-sets containing a fixed (l + 1)-set.
Open problems of Paul Erdös in graph theory
  • F. Graham
  • Computer Science
    J. Graph Theory
  • 1997
TLDR
The main treasure that Paul Erdős has left us is his collection of problems, most of which are still open today, and here is an attempt to collect and organize these problems in the area of graph theory.
Proof of the Erdős matching conjecture in a new range
AbstractLet s > k ≧ 2 be integers. It is shown that there is a positive real ε = ε(k) such that for all integers n satisfying (s + 1)k ≦ n < (s + 1)(k + ε) every k-graph on n vertices with no more
On unavoidable graphs
TLDR
Bounds are obtained which are in many cases asymptotically best possible and prove that there exists an (n, e)-unavoidable graph on ni edges.
Intersection Theorems for Systems of Sets
TLDR
A new upper bound is obtained for φ(2, k) for all k ⩾ 3 and a new lower bound forπ(n, 3) is obtained, both for positive integers n and k.
Unavoidable Stars in 3-Graphs
  • F. Graham
  • Computer Science
    J. Comb. Theory, Ser. A
  • 1983
TLDR
It is proved that, for k even, f(n, k) = k(k 3/2) n + F(n + k’).
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