论文标题
Ramsey数量的粉丝数量改善了
Improved bounds on the Ramsey number of fans
论文作者
论文摘要
对于给定的图形$ H $，Ramsey Number $ r（h）$是最低$ n $，因此，完整图的任何2边彩色$ k_n $都会产生$ h $的单色副本。给定一个正整数$ n $，a \ emph {fan} $ f_n $是由$ n $ triangles形成的图表，共享一个常见的顶点。我们表明，对于任何$ n $，$ {9n}/{2} -5 \ le r（f_n）\ le {11n}/{2} + 6 $。这改善了以前的最佳界限$ r（f_n）\ le 6n $ lin and li and $ r（f_n）\ ge 4n+2 $ of Zhang，Broersma和Chen。
For a given graph $H$, the Ramsey number $r(H)$ is the minimum $N$ such that any 2-edge-coloring of the complete graph $K_N$ yields a monochromatic copy of $H$. Given a positive integer $n$, a \emph{fan }$F_n$ is a graph formed by $n$ triangles that share one common vertex. We show that ${9n}/{2}-5\le r(F_n)\le {11n}/{2} + 6$ for any $n$. This improves previous best bounds $r(F_n) \le 6n$ of Lin and Li and $r(F_n) \ge 4n+2$ of Zhang, Broersma and Chen.
