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must have at least vertices). This bound can be tightened slightly: in every triangle-free graph there exists an independent set of vertices, and in some triangle-free graphs every independent set has vertices. One way to generate triangle-free graphs in which all independent sets are small is the triangle-free process in which one generates a maximal triangle-free graph by repeatedly adding randomly chosen edges that do not complete a triangle. With high probability, this process produces a graph

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