Choosability and fractional chromatic numbers Original Research Article

A graph G is (a, b)-choosable if for any assignment of a list of a colors to each of its vertices there is a subset of b colors of each list so that subsets corresponding to adjacent vertices are disjoint. It is shown that for every graph G, the minimum ratio ab where a, b range over all pairs of integers for which G is (a,b)-choosable is equal to the fractional chromatic number of G.