Definition
Let Ka,b denote a complete bipartite graph with a vertices on one side of the bipartition and b vertices on the other side. Define Za,b(m,n) to be the smallest integer k such that every bipartite graph that has m vertices on one side of its bipartition, n vertices on the other side, and k edges contains a subgraph isomorphic to Ka,b.
An alternative and equivalent definition is that Za,b(m,n) is the smallest integer k such that every (0,1)-matrix of size m × n with k 1's must have a set of a rows and b columns such that the corresponding a×b submatrix is made up only of 1's.
For the specific case when m = n and a = b the shorter notation Za(n) = Za,b(m,n) may also be used.
Read more about this topic: Zarankiewicz Problem
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