Lower bounds for Turán's problem
✍ Scribed by Peter Frankl; Vojtěch Rödl
- Book ID
- 110567484
- Publisher
- Springer Japan
- Year
- 1985
- Tongue
- English
- Weight
- 138 KB
- Volume
- 1
- Category
- Article
- ISSN
- 0911-0119
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
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.
For i = 1,2 .... ,k, let Gi be a graph with vertex set [n] = {1 .... ,n} containing no Fi as a subgraph. At most how many edges are in G1 t3 -• • U Gk? We shall answer this Turfin-Ramseytype question asymptotically, and pose a number of related problems. Given graphs F1 ..... Fk, write exk(n,F 1 ..