List coloring of Cartesian products of graphs

A well-established generalization of graph coloring is the concept of list coloring. In this setting, each vertex v of a graph G is assigned a list L(v) of k colors and the goal is to find a proper coloring c of G with c(v)@?L(v). The smallest integer k for which such a coloring c exists for every choice of lists is called the list chromatic number of G and denoted by @g"l(G). We study list colorings of Cartesian products of graphs. We show that unlike in the case of ordinary colorings, the list chromatic number of the product of two graphs G and H is not bounded by the maximum of @g"l(G) and @g"l(H). On the other hand, we prove that @g"l(GxH)=