一個不含K_2,2的二分極圖是一個含有最多邊數且不含有子圖K_2,2的二分圖。若此二分圖為K_m,n的子圖,則求此二分極圖的邊數的問題也就是出名的Zarankiewicz問題。在本論文中,我們令g(m,n)為K_m,n中不含K_2,3的二分極圖的邊數。我們得到一些結果。 An extremal K_2,2-free bipartite graphs is a bipartite graph which contains the maximum number of edges and does not contain any subgraph K_2,2 . If this bipartite graph is a subgraph of K_m,n, then finding the number of edges of the extremal bipartite graph is the well-known Zarankiewicz Problem . In this thesis , we let be the number of edges of the extremal K_2,3-free bipartite graph which is a subgraph of K_m,n .We obtain some results.