On the Turán number for the hexagon
✍ Scribed by Zoltan Füredi; Assaf Naor; Jacques Verstraëte
- Book ID
- 108051446
- Publisher
- Elsevier Science
- Year
- 2006
- Tongue
- English
- Weight
- 219 KB
- Volume
- 203
- Category
- Article
- ISSN
- 0001-8708
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
For a family of r-graphs F; the Tur! a an number exðn; FÞ is the maximum number of edges in an n vertex r-graph that does not contain any member of F: The Tur! a an density When F is an r-graph, pðFÞ=0; and r > 2; determining pðFÞ is a notoriously hard problem, even for very simple r-graphs F: For
A system of r-element subsets (blocks) of an n-element set X n is called a Tura n (n, k, r)-system if every k-element subset of X n contains at least one of the blocks. The Tura n number T(n, k, r) is the minimum size of such a system. We prove upper estimates: + as n Ä , r Ä , k=(#+o(1))r, #>1.
An algebraic construction implies lim n Ä ex(n, K 2, t+1 ) n &3Â2 =-tÂ2. 1996 Academic Press, Inc. 1 2 -t n 3Â2 +(nÂ4). To prove the Theorem we obtain a matching lower bound from a construction closely related to the examples from [ERS] and [B], and inspired by an example of Hylte n Cavallius [H] an