Gallai-Ramsey numbers for monochromatic $K_4^{+}$ or $K_3$

Abstract

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 that $s\le k$, the $k$-colored Gallai-Ramsey number $g{r}_k(K_3:s\cdot H,(k-s)\cdot G)$ 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 $g{r}_k(K_3:K_4^{+})$ is obtained.

18 pages

Cited by in corpus (1)

• Gallai-Ramsey numbers for graphs with five vertices and eight edges