Zarankiewicz Problem

In the mathematical field of extremal graph theory, the Zarankiewicz problem asks how many edges can be added to a bipartite graph while avoiding a specific bipartite subgraph. Initially, the Polish mathematician Kazimierz Zarankiewicz proposed the problem of determining the maximum number of edges in an n-vertex graph with no complete bipartite graph K_3,3 as a subgraph, for n ≤ 6; that is, in later notation, he asked for the values of the function Z₃(n). The Kővári–Sós–Turán theorem gives a bound on the Zarankiewicz problem when the subgraph to be avoided is a complete bipartite graph.