List-coloring graphs without -minors

Abstract: In this note, it is shown that every graph with no -minor is -list-colorable. We also give an extremal function for the existence for a -minor. Our proof implies that there is a linear time algorithm for showing that either has a -minor or is -choosable. In fact, if the latter holds, then the algorithm gives rise to a -list-coloring. [Copyright &y& Elsevier]