Let G be a finite simple graph. Then χ(G) is its chromatic number, ∆(G) is its maximum degree, and ω(G) is its clique number. For any graph G, χ(G) ≥ ω(G). On the other hand, it is easy to see that G can be coloured greedily, one vertex at a time, with ∆(G)+1 colours. In , Reed considered the problem of bounding χ(G) from above by convex combination
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