2-Colored triangles in edge-colored complete graphs, II |
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Authors: | D T Busolini |
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Institution: | Mathematics Group, The Hatfield Polytechnic, P. O. Box 109, College Lane, Hatfield, Herts, United Kingdom |
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Abstract: | The largest number n = n(k) for which there exists a k-coloring of the edges of kn with every triangle 2-colored is found to be n(k) = 2r5m, where k = 2m + r and r = 0 or 1, and all such colorings are given. We also prove the best possible result that a k-colored Kp satisfying 1 < k < 1 + √p contains at most k − 2 vertices not in a bichromatic triangle. |
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