On a theorem of Erdos, Rubin, and Taylor on choosability of complete bipartite graphs

Erdos, Rubin, and Taylor found a nice correspondence between the minimum order of a complete bipartite graph that is not r-choosable and the minimum number of edges in an r-uniform hypergraph that is not 2-colorable (in the ordinary sense). In this note we use their ideas to derive similar correspondences for complete k partite graphs and complete k-uniform k-partite hypergraphs.