Upper Bounds for Turán Numbers
1997, Journal of Combinatorial Theory, Series A
https://doi.org/10.1006/JCTA.1996.2739Abstract
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: T(n, r+1, r) (1+o(1)
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