Turán number

In mathematics, the Turán number ${\displaystyle T(n,k,r)}$ for ${\displaystyle r}$-uniform hypergraphs of order ${\displaystyle n}$ is the smallest number of ${\displaystyle r}$-edges such that every induced subgraph on ${\displaystyle k}$ vertices contains an edge. This number was determined for ${\displaystyle r=2}$ by Turán (1941), and the problem for general ${\displaystyle r}$ was introduced in Turán (1961). The paper (Sidorenko 1995) gives a survey of Turán numbers.