A lower bound for set‐coloring Ramsey numbers

Abstract The set‐coloring Ramsey number is defined to be the minimum such that if each edge of complete graph assigned a set colors from , then one contains monochromatic clique size . case usual ‐color number, and was studied by Erdős, Hajnal Rado in 1965, Erdős Szemerédi 1972. first significant results for general were obtained only recently, Conlon, Fox, He, Mubayi, Suk Verstraëte, who showed bounded away 0 1. In range however, their upper lower bounds diverge significantly. this note we introduce new (random) coloring, use it determine up polylogarithmic factors exponent essentially all