On the fractional chromatic number, the chromatic number, and graph products

It is shown that the difference between the chromatic number chi and the fractional chromatic number chi(f) can be arbitrarily large in the class of uniquely colorable, vertex transitive graphs. For the lexicographic product G o H it is shown that chi(G o H) greater than or equal to chi(f)(G) chi(H). This bound has several consequences, in particular, it unifies and extends several known lower bounds. Lower bounds of Stahl (for general graphs) and of Bollobas and Thomason (fur uniquely colorable graphs) are also proved in a simple, elementary way. (C) 2002 Elsevier Science B.V. All rights reserved.