The maximum possible weight of a fractional clique of a graph G is called the fractional clique number of G, denoted ω^*(G) (Godsil and Royle 2001, pp. 136-137) or ω_F . Every simple graph has a fractional clique number which is a rational number or integer. The fractional clique number satisfies ω(G)<=ω^*(G) = χ^*(G)<=χ(G), where ω(G) is the clique number, χ^*(G) is the fractional chromatic number, and χ(G) is the chromatic number, where the result ω^*(G) = χ^*(G) follows from the strong duality theorem for linear programming .
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