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摘要
For a simple graph G, let \chif (G) be the fractional chromatic number of G. In this paper, we aim to establish upper bounds on \chif (G) for those graphs G with restrictions on the clique number. Namely, we prove that for \Delta \geq 4, if G has maximum degree at most \Delta and is K =-free, then \chif (G) \leq \Delta -81 unless G = C82 or G = C5 \boxtimes K2. This improves the result in [A. King, L. Lu, and X. Peng, SIAM J. Discrete Math., 26 (2012), pp. 452--471] for \Delta \geq 4 and the result in [K. Edwards and A. D. King, SIAM J. Discrete Math., 27 (2013), pp. 1184--1208] for \Delta \in {6, 7, 8}.
