---
tag: J94HMG0SG6
kind: problem
name: Ruzsa–Szemerédi problem
aliases: [6-3-problem]
sources:
  - wikipedia: en:59842050@r1358233720
    locator: Ruzsa–Szemerédi problem
    note: adopted
    mention: wikipedia://en/59842050
    sections: [Problem]
same_as:
  wikidata: Q62760546
  wikipedia: Ruzsa–Szemerédi problem
inventory: [W48E8EN983]
---

## Problem

In [[combinatorial mathematics|0JKW7W7XFR]] and extremal graph theory, the **Ruzsa–Szemerédi problem** or **(6,3)-problem** asks for the maximum number of edges in a graph in which every edge belongs to a unique triangle. Equivalently it asks for the maximum number of edges in a balanced bipartite graph whose edges can be partitioned into a linear number of induced matchings, or the maximum number of triples one can choose from $n$ points so that every six points contain at most two triples. The problem is named after Imre Z. Ruzsa and Endre Szemerédi, who first proved that its answer is smaller than $n^2$ by a slowly-growing (but still unknown) factor.