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Let S be a set of N points on the plane in general position, colored arbitrarily with c colors ( $$c\in {\mathbb {N}}$$ c ∈ N ). A subset of points is said to be monochromatic if all its points have the same color. In this paper we show that if N is sufficiently large, then S contains a monochromatic triangle with vertices in S and containing at most $$c-3$$ c - 3 points in its...