讲座内容：

For a simple graph G, let \chi_f(G) be the fractional chromatic number of G. In this talk, we prove that for \Delta \geq 4, if G has maximum degree at most \Delta and is K_{\Delta}-free, then \chi_f(G) \leq \Delta-\frac{1}{8} unless G= C^2_8 or G = C_5\boxtimes K_2. This improves the result in [King, Lu, and Peng, SIAM J. Discrete Math., 26(2) (2012), pp. 452-471] for \Delta \geq 4 and the result in [Katherine and King, SIAM J. Discrete Math., 27(2) (2013), pp. 1184-1208] for \Delta \in \{6,7,8\}.