The Sylvester-Gallai theorem, colourings and algebra

Abstract

Our point of departure is the following simple common generalisation of the Sylvester-Gallai theorem and the Motzkin-Rabin theorem: Let S be a finite set of points in the plane, with each point coloured red or blue or with both colours. Suppose that for any two distinct points A, B ∈ S sharing a colour there is a third point C ∈ S, of the other colour… (More)
DOI: 10.1016/j.disc.2007.12.027

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