  In 2001, Woodall conjectured that for every pair of integers $s,t \ge 1$, all
graphs without a $K_{s,t}$-minor are $(s+t-1)$-choosable. In this note we
refute this conjecture in a strong form: We prove that for every choice of
constants $\varepsilon>0$ and $C \ge 1$ there exists $N=N(\varepsilon,C) \in
\mathbb{N}$ such that for all integers $s,t $ with $N \le s \le t \le Cs$ there
exists a graph without a $K_{s,t}$-minor and list chromatic number greater than
$(1-\varepsilon)(2s+t)$.
