Topological Minors in Bipartite Graphs

For a bipartite graph G on m and n vertices, respectively, in its vertices classes, and for integers s and t such that 2 <= s <= t, 0 <= m - s <= n - t, and m + n <= 2s + t - 1, we prove that if G has at least mn - (2(m - s) + n - t) edges then it contains a subdivision of the complete bipartite K((s,t)) with s vertices in the m-class and t vertices in the n-class. "Furthermore, we characterize the corresponding extremal bipartite graphs with mn - (2(m - s) + n - t + 1) edges for this topological Turan type problem.