Gallai‐Ramsey number for K4.

Given a graph H, the k‐colored Gallai‐Ramsey number grk(K3⁢ :H) is defined to be the minimum integer n such that every k‐coloring (using all k colors) of the complete graph on n vertices contains either a rainbow triangle or a monochromatic copy of H. Recently, Fox et al [J. Combin. Theory Ser. B, 111 (2015), pp. 75–125] conjectured the value of the Gallai‐Ramsey numbers for complete graphs. We verify this conjecture for the first open case, where H=K4. [ABSTRACT FROM AUTHOR]