论文标题
加莱·拉姆齐（Gallai Ramsey）的双星号
Gallai Ramsey number for double stars
论文作者
论文摘要
鉴于图$ g $和一个正整数$ k $，\ emph {gallai-ramsey number}被定义为最小数量的顶点$ n $，因此$ k_n $的任何$ k $ - edge颜色都包含彩虹（所有不同的颜色）$ g $ of $ g $或$ g $的单色副本。在本文中，我们在Double Stars $ s（n，m）$的Gallai-Ramsey数字上获得了一般的上限和下限，其中$ s（n，m）$是从两星$ k_ {1，n} $和$ k_ {1，m} $的图表中获得的图，通过在其中心之间添加一个边缘。在某些情况下，我们还提供了鲜明的结果。
Given a graph $G$ and a positive integer $k$, the \emph{Gallai-Ramsey number} is defined to be the minimum number of vertices $n$ such that any $k$-edge coloring of $K_n$ contains either a rainbow (all different colored) copy of $G$ or a monochromatic copy of $G$. In this paper, we obtain general upper and lower bounds on the Gallai-Ramsey numbers for double stars $S(n,m)$, where $S(n,m)$ is the graph obtained from the union of two stars $K_{1,n}$ and $K_{1,m}$ by adding an edge between their centers. We also provide the sharp result in some cases.
