On Ks,t-minors in graphs with given average degree, II

Let Ks,t∗ denote the graph obtained from Ks,t by adding all edges between the s vertices of degree t in it. We show how to adapt the argument of our previous paper [A.V. Kostochka, N. Prince, On Ks,t-minors in graphs with given average degree, Discrete Math. 308 (2008) 4435-4445] to prove that if t/log2t≥1000s, then every graph G with average degree at least t+8slog2s has a Ks,t∗ minor. This refines a corresponding result by Kühn and Osthus.