Complete Bipartite Free Graphs

Abstract

The study of the maximum size $ex(n;K_{t,t})$ of a graph of order $n$ not containing the complete bipartite graph $K_{t,t}$ as a subgraph is the aim of this paper. We show an upper bound for this extremal function that is optimum for infinitely many values of $n$ and $t$. Moreover, we characterize the corresponding family of extremal graphs.