论文标题
对ł核的连接匹配方法的改进
An improvement on Łuczak's connected matchings method
论文作者
论文摘要
图$ g $中的连接匹配是$ g $的连接组件中包含的匹配。由于核的一种众所周知的方法，可以在几乎完整的图中降低有关单色路径和循环的问题。我们表明，这些可以进一步简化为有关单色连接匹配的问题。 我们通过展示如何使用比Gyárfás，Ruszinkin，Sárközy和Szemerédi（2007）更简单的参数来说明如何使用它来确定$ 3 $ - 颜色的拉姆西数量的长路径的潜力，从而说明了这种新减少的潜力。
A connected matching in a graph $G$ is a matching contained in a connected component of $G$. A well-known method due to Łuczak reduces problems about monochromatic paths and cycles in complete graphs to problems about monochromatic connected matchings in almost complete graphs. We show that these can be further reduced to problems about monochromatic connected matchings in complete graphs. We illustrate the potential of this new reduction by showing how it can be used to determine the $3$-colour Ramsey number of long paths, using a simpler argument than the original one by Gyárfás, Ruszinkó, Sárközy, and Szemerédi (2007).
