论文标题
对角线拉姆西通过有效的quasirandomness
Diagonal Ramsey via effective quasirandomness
论文作者
论文摘要
我们将对角线拉姆西编号的上限提高到\ [r（k+1，k+1）\ le \ exp（-c（\ log k）^2）\ binom {2k} {2k} {k} {k} \] $ k \ ge 3 $。为此，我们建立在托马森（Thomason）和康隆（Conlon）延伸的拉姆齐（Ramsey）数字的quasirandomness和诱导框架的基础上，展示了有关图形收敛性的最佳“有效quasirandomness”结果。这种最优性代表了改进的自然障碍。
We improve the upper bound for diagonal Ramsey numbers to \[R(k+1,k+1)\le\exp(-c(\log k)^2)\binom{2k}{k}\] for $k\ge 3$. To do so, we build on a quasirandomness and induction framework for Ramsey numbers introduced by Thomason and extended by Conlon, demonstrating optimal "effective quasirandomness" results about convergence of graphs. This optimality represents a natural barrier to improvement.
