Gallai-Ramsey Numbers for Monochromatic K_4^+ or K_3 - Su, Xueli; Liu, Yan (Discontinuity, Nonlinearity, and Complexity, 2026)
A Gallai k-coloring is a k-edge coloring of a complete graph in which there are no rainbow triangles. For two given graphs H, G and two positive integers k,s with s≤ k, the k-colored Gallai-Ramsey number gr_k(K_3: s· H, (k-s)· G) is the minimum integer n such that every Gallai k-colored K_n contains a monochromatic copy of H colored by one of the first s colors or a monochromatic copy of G colored by one of the remaining k-s colors. In this paper, we determine the value of Gallai-Ramsey number in the case that H=K_4^+ and G=K_3. Thus the Gallai-Ramsey number gr_k(K_3: K_4^+) is obtained.