Abstract
By applying a look-ahead algorithm, we show that there are, up to isomorphism, exactly two colorings of the edges of K 15 with three colors which do not contain a monochromatic triangle. Based on this result we derive a new upper bound for the three color Ramsey number, R(4, 3, 3) ⩽ 32. The best previously known bounds were 30⩽ R(4,3,3)⩽33.
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