Zs. Tuza and M. Voigt, Every 2-choosable graph is (2m,m)-choosable, J. Graph Theory 22 (1996), 245-252.
Zs. Tuza and M. Voigt, On a conjecture of Erdős, Rubin and Taylor, Tatra Mountains Math. Publ. 9 (1996), 69-82.
From the Abstract of the last mentioned paper:
In 1979, Erdős, Rubin and Taylor raised the conjecture that every (a,b)-choosable graph G is also (am,bm)-choosable for all m>1. We investigate the case b=1, presenting some classes of (a,1)-choosable graphs for which (am,m)-choosability can be proved for all m.
Recently a long, interesting and very informative survey has appeared:
Zs. Tuza, Graph Colorings with Local Constraints - A Survey, to appear in Discussiones Mathematicae Graph Theory 17 (1997), Manuscript, 67 pages.
August 14, 1997. Bjarne Toft