论文标题
拉姆齐数量的大量偶数周期和粉丝
Ramsey numbers of large even cycles and fans
论文作者
论文摘要
对于Graphs $ f $和$ h $，Ramsey Number $ r（f，h）$是最小的正整数$ n $，因此任何红色/蓝色边缘颜色的$ k_n $都包含红色$ f $或蓝色$ h $。令$ c_n $为长度$ n $，$ f_n $的周期为粉丝，由$ n $三角形组成，所有这些都共享一个共同的顶点。在本文中，我们证明，对于所有足够大的$ n $，\ [r（c_ {2 \ lfloor an \ rfloor}，f_n）= \ left \ {\ oken {arnay} {array} {ll} {ll} {ll}（2+2a+o（2+2a+o（1））n＆\ textrm （4a+o（1））N＆\ textrm {如果$ a \ geq 1 $。} \ end {array} \ right。 \]
For graphs $F$ and $H$, the Ramsey number $R(F, H)$ is the smallest positive integer $N$ such that any red/blue edge coloring of $K_N$ contains either a red $F$ or a blue $H$. Let $C_n$ be a cycle of length $n$ and $F_n$ be a fan consisting of $n$ triangles all sharing a common vertex. In this paper, we prove that for all sufficiently large $n$, \[ R(C_{2\lfloor an\rfloor}, F_n)= \left\{ \begin{array}{ll} (2+2a+o(1))n & \textrm{if $1/2\leq a< 1$,}\\ (4a+o(1))n & \textrm{if $ a\geq 1$.} \end{array} \right. \]
