---
tag: M09T8TFVWF
kind: concept
name: Turán number
aliases: [turan-system]
sources:
  - wikipedia: en:14982946@r1354036835
    locator: Turán number
    note: adopted
    mention: wikipedia://en/14982946
    sections: [Summary]
same_as:
  wikidata: Q7856597
  wikipedia: Turán number
inventory: [JCGS7X7GBP]
---

## Summary

In mathematics, the **Turán number** $T(n,k,r)$ for $r$-uniform hypergraphs of order $n$ is the smallest number of $r$-edges such that every [[induced subgraph|0EREPBVG2G]] on $k$ vertices contains an edge. This number was determined for $r = 2$ by (Turán 1941), and the problem for general $r$ was introduced in (Turán 1961). The paper (Sidorenko 1995) gives a survey of Turán numbers.