page_title: Ruzsa–Szemerédi problem
hierarchical_section_title: Ruzsa–Szemerédi problem
context_page_description: In combinatorial mathematics and extremal graph theory, the Ruzsa–Szemerédi problem or-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 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 by a slowly-growing factor.
context_section_description: In combinatorial mathematics 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  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  by a slowly-growing (but still unknown) factor.
caption: The nine-vertex Paley graph, a balanced tripartite graph with 18 edges, each belonging to exactly one triangle