The extremal function for unbalanced bipartite minors Original Research Article

We consider the question of what average degree forces a graph to have a Ks,t minor, for s fixed and t sufficiently large. In the case of s=2, we show that if t is sufficiently large and G is a graph with more than ((t+1)/2)(|G|−1) edges then G has a K2,t minor. This result is best possible for |G|≡1 (mod t).