Zarankiewicz problem

Unsolved problem in mathematics
What is the largest possible number of edges in a bipartite graph that has a given number of vertices and has no complete bipartite subgraphs of a given size?
More unsolved problems in mathematics

The Zarankiewicz problem, an unsolved problem in mathematics, asks for the largest possible number of edges in a bipartite graph that has a given number of vertices and has no complete bipartite subgraphs of a given size. It belongs to the field of extremal graph theory, a branch of combinatorics, and is named after the Polish mathematician Kazimierz Zarankiewicz, who proposed several special cases of the problem in 1951.

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