\(C_4\)-saturated bipartite graphs (Q1861219)

The authors consider the problem of finding subgraphs of the complete bipartite graph \(K_{m,n}\) which do not contain a subgraph isomorphic to a copy of \(K_{s,t}\) and are maximal with respect to this property. They translate this problem to the terminology of partial block designs. Their main interest concerns the case of \(s=t=2\) in which they apply some simple facts from the design theory to give alternate proofs of some classic asymptotic results on the Zarankiewicz problem due to Bollobás.