On -minors in graphs with given average degree, II

Let K s , t ∗ denote the graph obtained from K s , 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 K s , t -minors in graphs with given average degree, Discrete Math. 308 (2008) 4435–4445] to prove that if t / log 2 t ≥ 1000 s , then every graph G with average degree at least t + 8 s log 2 s has a K s , t ∗ minor. This refines a corresponding result by Kühn and Osthus.