论文标题
随机着色过程可改善对广义Ramsey数字的Erdős-Gyárfás问题的界限
A random coloring process gives improved bounds for the Erdős-Gyárfás problem on generalized Ramsey numbers
论文作者
论文摘要
erdős-gyárfás数字$ f（n，p，q）$是为完整图$ k_n $的边缘上色所需的最小颜色，因此其所有$ p $ clique-clique-clique-clique跨度至少至少$ q $颜色。在本文中，我们改善了$ f（n，p，q）$ $ p，q $和大型$ n $的最著名的上限（n，p，q）$。我们的证明使用随机着色过程，我们使用所谓的微分方程方法来分析该过程来建立动态浓度。
The Erdős-Gyárfás number $f(n, p, q)$ is the smallest number of colors needed to color the edges of the complete graph $K_n$ so that all of its $p$-clique spans at least $q$ colors. In this paper we improve the best known upper bound on $f(n, p, q)$ for many fixed values of $p, q$ and large $n$. Our proof uses a randomized coloring process, which we analyze using the so-called differential equation method to establish dynamic concentration.
