Ramsey-Type Problem for an Almost Monochromatic $K_4$

Jacob Fox, Benny Sudakov
2009 SIAM Journal on Discrete Mathematics  
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