论文标题
单色$ k_4^{+} $或$ k_ {3} $的gallai-ramsey数字
Gallai-Ramsey numbers for monochromatic $K_4^{+}$ or $K_{3}$
论文作者
论文摘要
Gallai $ k $ - 颜色是$ k $ - 边缘的完整图形，其中没有彩虹三角形。对于两个给定的图，$ h，g $和两个正整数$ k，s $，其中$ s \ leq k $，$ k $ - 颜色的gallai-ramsey number $ gr_ gr_ {k {k_ {3}：s \ cdot h，〜（k s） $ h $的单色副本，由第一个$ s $颜色之一或剩下的$ k-s $颜色之一的$ g $的单色副本或单色副本。在本文中，我们确定了加莱 - 拉姆西号的值，如果$ h = k_ {4}^{+} $和$ g = k_ {3} $。因此，获得Gallai-Ramsey编号$ gr_ {k}（k_ {3}：k_ {4}^{+}）$。
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 $s\leq k$, the $k$-colored Gallai-Ramsey number $gr_{k}(K_{3}: s\cdot H,~ (k-s)\cdot G)$ 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 $gr_{k}(K_{3}: K_{4}^{+})$ is obtained.
