期刊
SIAM JOURNAL ON DISCRETE MATHEMATICS
卷 37, 期 4, 页码 2486-2507出版社
SIAM PUBLICATIONS
DOI: 10.1137/21M1440037
关键词
coloring; fractional coloring; fractional chromatic number
This paper aims to establish upper bounds on the fractional chromatic number of graphs with restrictions on the clique number. The results show that for certain conditions, the upper bound of the fractional chromatic number is improved compared to previous research.
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}.
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