Ramsey路径数
Ramsey Numbers of Trails
摘要：
我们开始研究拉姆齐数的痕迹。令$k \geq 2$为正整数。具有$k$顶点的踪迹的Ramsey数被定义为最小数目$n$，使得对于每个具有$n$顶点的图$H$，$H$或完全$\overline{H}$包含具有$k$顶点的踪迹。证明了以$k$为顶点的轨迹的Ramsey数至多为$k$且至少为$2\sqrt{k}+Θ(1)$ .这改进了$\lfloor 3k/2\rfloor -1$的平凡上界。
英文摘要：
We initiate the study of Ramsey numbers of trails. Let $k \geq 2$ be a positive integer. The Ramsey number of trails with $k$ vertices is defined as the the smallest number $n$ such that for every graph $H$ with $n$ vertices, $H$ or the complete $\overline{H}$ contains a trail with $k$ vertices. We prove that the Ramsey number of trails with $k$ vertices is at most $k$ and at least $2\sqrt{k}+Θ(1)$. This improves the trivial upper bound of $\lfloor 3k/2\rfloor -1$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
