High Quality Content by WIKIPEDIA articles! 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 K. Zarankiewicz proposed the problem of determining the maximum number of edges in an n-vertex graph with no complete bipartite graph K3,3 as a subgraph, for n <= 6; that is, in later notation, he asked for the values of the function Z3(n). The Kovari–Sos–Turan theorem gives a bound on the Zarankiewicz problem when the subgraph to be avoided is a complete bipartite graph.

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