It is shown that the difference between the chromatic number x and the fractional chromatic number x_f can be arbitrarity large in the class of uniquely colorable, vertex transitive graphs. For the lexicographic product G o H it is shown that x(G o H) ≥ x_f(G)x(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 (for uniquely colorable graphs) are also proved in a simple, elementary way.
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机译：结果表明，在唯一可着色的顶点传递图类中，色数x和分数色数x_f之间的差可以任意大。对于词典产品G o H，表明x（G o H）≥x_f（G）x（H）。该界限具有多个后果，尤其是它统一并扩展了几个已知的下界。 Stahl（对于一般图形）以及Bollobas和Thomason（对于唯一可着色图形）的下限也可以通过简单的基本方法得到证明。
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