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.