An Improvement to Mathon's Cyclotomic Ramsey Colorings

Xiaodong Xu, Stanisław P. Radziszowski


In this note we show how to extend Mathon's cyclotomic colorings of the edges of some complete graphs without increasing the maximum order of monochromatic complete subgraphs. This improves the well known lower bound construction for multicolor Ramsey numbers, in particular we obtain $R_3(7) \ge 3214$.

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