Abstract
The largest number n = n( k) for which there exists a k-coloring of the edges of k n with every triangle 2-colored is found to be n( k) = 2 r 5 m , where k = 2 m + r and r = 0 or 1, and all such colorings are given. We also prove the best possible result that a k-colored K p satisfying 1 < k < 1 + √ p contains at most k − 2 vertices not in a bichromatic triangle.
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