论文标题
随机图中的拉姆西数量
Ramsey numbers of cycles in random graphs
论文作者
论文摘要
令$ r（c_n）$为$ n $顶点上的循环的拉姆齐号。我们证明，对于$ c> 0 $，只要$ g（n，p）$的边缘每$ 2 $颜色的概率高，只要$ n \ geq r（c_n） + c/p $和$ p \ egq c/n $。这是$ C $的敏锐价值，它改善了莱茨特和克里维尔维奇，克罗伦贝格和蒙德的结果。
Let $R(C_n)$ be the Ramsey number of the cycle on $n$ vertices. We prove that, for some $C > 0$, with high probability every $2$-colouring of the edges of $G(N,p)$ has a monochromatic copy of $C_n$, as long as $N\geq R(C_n) + C/p$ and $p \geq C/n$. This is sharp up to the value of $C$ and it improves results of Letzter and of Krivelevich, Kronenberg and Mond.
