论文标题
关于在拉姆西理论中使用发件人的不对称群体的使用
On the use of senders for asymmetric tuples of cliques in Ramsey theory
论文作者
论文摘要
图形$ g $是$ q $ -ramsey，用于$ q $ - 图形$（H_1，\ ldots，h_q）$，如果每$ q $ - $ g $的每一个颜色的$ g $的颜色都存在单色$ h_i $ i $ i $ i $ i $ i \ in [q]的单色副本。在过去的几十年中，研究人员调查了许多与此概念有关的问题，旨在了解固定元组的图形属性。在研究这种类型问题时开发的工具中有小工具图，称为信号发件人和确定词，这对于构建具有某些属性的Ramsey图非常宝贵。但是，到目前为止，这些小工具已被证明存在并主要用于两色设置或对称的多色环境，而我们对它们对多色不对称元素的存在的了解非常有限。在本文中，我们为任何集团元组构建了此类小工具。然后，我们使用这些小工具将该区域的三个经典定理概括为不对称的多色设置。
A graph $G$ is $q$-Ramsey for a $q$-tuple of graphs $(H_1,\ldots,H_q)$ if for every $q$-coloring of the edges of $G$ there exists a monochromatic copy of $H_i$ in color $i$ for some $i\in[q]$. Over the last few decades, researchers have investigated a number of questions related to this notion, aiming to understand the properties of graphs that are $q$-Ramsey for a fixed tuple. Among the tools developed while studying questions of this type are gadget graphs, called signal senders and determiners, which have proven invaluable for building Ramsey graphs with certain properties. However, until now these gadgets have been shown to exist and used mainly in the two-color setting or in the symmetric multicolor setting, and our knowledge about their existence for multicolor asymmetric tuples is extremely limited. In this paper, we construct such gadgets for any tuple of cliques. We then use these gadgets to generalize three classical theorems in this area to the asymmetric multicolor setting.
