At Least Half Of All Graphs Satisfy χ\leq {1/4}ω+ {3/4}Δ+ 1

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We prove that for any graph G at least one of G or $\bar{G}$ satisfies $χ\leq {1/4}ω+ {3/4}Δ+ 1$. In particular, self-complementary graphs satisfy this bound.

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