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Abstract or Description

In 1959, Goodman [9] determined the minimum number of monochromatic triangles in a complete graph whose edge set is 2-coloured. Goodman (1985) [10] also raised the question of proving analogous results for complete graphs whose edge sets are coloured with more than two colours. In this paper, for n sufficiently large, we determine the minimum number of monochromatic triangles in a 3-coloured copy of Kn. Moreover, we characterise those 3-coloured copies of Kn that contain the minimum number of monochromatic triangles.



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Published In

Journal of Combinatorial Theory, Series B, 103, 4, 489-503.