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In this short note we prove that there is a constant c such that every k-edge-coloring of the complete graph K n with n ≥ 2 ck contains a K 4 whose edges receive at most two colors. This improves on a result of Kostochka and Mubayi, and is the first exponential bound for this problem.doi:10.1137/070706628 fatcat:y6hzzyfcxnaibcyvhsqbncumbe